## 物理代写|力学代写mechanics代考|TLIB2003

statistics-lab™ 为您的留学生涯保驾护航 在代写力学mechanics方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写力学mechanics代写方面经验极为丰富，各种代写力学mechanics相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• Advanced Probability Theory 高等概率论
• Advanced Mathematical Statistics 高等数理统计学
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 物理代写|力学代写mechanics代考|Anisotropic Materials

In optically anisotropic (birefringent) materials the change of the stress-optical path of a light ray is different along the directions of the two in-plane principal stresses $\sigma_1$ and $\sigma_2$. This change is given by Eq. (6.36) for the rays transmitted through the specimen and by Eq. (6.43) for the rays reflected from the rear face of the specimen. The plus (+) and minus (-) signs in these equations correspond to the two principal stresses. In such materials, two caustics are formed corresponding to the two principal stresses. Figure 6.17a, b presents the experimental double caustics at the crack tip formed by rays reflected from the rear face (a) and transmitted (b) through a specimen made of Polycarbonate of Bisphenol which is an optically anisotropic material. The specimen is loaded to opening mode.

Following the same procedure as in the case of optically isotropic materials presented previously, the opening-mode stress intensity factor $K_I$ can be determined from Eq. (6.61) using the transverse (t) or longitudinal (1) diameter $D_{t, l}$ of the caustic with the corresponding values of $\delta_t^{\max }$ or $\delta_l^{\max }$ (instead of $D$ and $\delta$, with $\mu=0$ ). The quantities $\delta_t^{\max }$ or $\delta_l^{\max }$ are functions of the anisotropy coefficient $\xi$ of the material. Figure 6.18 presents the variation of $\delta_t^{\max }$ and $\delta_l^{\max }$ versus $\xi$ for the transverse and longitudinal diameters of the caustic, respectively, for the outer and inner caustic.

## 物理代写|力学代写mechanics代考|The State of Stress Near the Crack Tip

The previous analysis of the method of caustics was based on the assumption that plane stress conditions apply in the neighborhood of the crack tip. The value of the stress-optical constant $c$ entered in Eqs. (6.55) and (6.60) for the determination of stress intensity factors $K_I, K_{I I}$ corresponds to plane stress conditions. However, the state of stress in the vicinity of the crack tip changes from plane strain very close to the tip to plane stress further away from the tip. Between these two regions, the stress field is three-dimensional. The value of $c$ changes when the state of stress changes from plane strain to plane stress. In order to use the correct value of $c$ for the determination of stress intensity factors $K_I, K_{I I}$ we should know the state of stress along the initial curve of the caustic.

It was established [3-10] that the state of stress becomes plane stress at distances $r$ from the crack tip larger than approximately half the specimen thickness. Thus, the radius of the initial curve of the caustic should be larger than half the specimen thickness $d, r_0>d / 2$. If $r_0<d / 2$ the initial curve lies in the region where the state of stress is three-dimensional and the plane stress value of $c$ does not apply. For the correct application of the method of caustics, the condition $r_0>d / 2$ should be satisfied. The radius of the initial curve $r_0$ can be determined from Eq. (6.51) after the determination of the stress intensity factor and the above condition should be checked. If the condition $r_0>d / 2$ is not satisfied the experiment should be considered invalid and should be repeated by changing the values of the dimensions of the optical setup and the applied loads.

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。

## 物理代写|力学代写mechanics代考|ENGR20004

statistics-lab™ 为您的留学生涯保驾护航 在代写力学mechanics方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写力学mechanics代写方面经验极为丰富，各种代写力学mechanics相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• Advanced Probability Theory 高等概率论
• Advanced Mathematical Statistics 高等数理统计学
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

Consider a transparent specimen illuminated by a parallel light beam and a screen at a distance $z_0$ downstream from the specimen placed parallel to the plane of the specimen (Fig. 6.9). A point $P$ on the specimen is imaged at point $P^{\prime}$ on the screen. It is assumed that the slopes of the surface are small and the distance $z_0$ is large compared to the change of the specimen thickness due to loading.

For the case of a transparent specimen the mapping equation of point $P$ to point $P^{\prime}$, according to Eq. $(6.5)$, is given by
\begin{aligned} & W_x=x-z_0 \frac{\partial(\Delta s)}{\partial x} \ & W_y=y-z_0 \frac{\partial(\Delta s)}{\partial y} \end{aligned}
where $\Delta s$ is the change of the optical path of a ray passing through the specimen due to loading.

For an optically inert material, $\Delta s$ is given by Eq. (6.37) for the light rays traversing the specimen and by Eq. (6.44) for the light rays reflected from the rear face of the transparent specimen. For the rays reflected from the front face of the specimen the stress-optical constant $c_t$ in Eq. (6.37) should be replaced by the ratio $v / E(v$ is the Poisson’s ratio and $E$ is the modulus of elasticity). For all three cases of light rays traversing the specimen, reflected from the rear face or from the front face of the specimen the transformation Fq. (6.45) applies with different valnes of the stress-optical constant $\mathrm{c}$, which takes the values $c_t, 2 c_r$, or $v / E$, respectively.

The singular polar stresses at the tip of the crack for opening-mode loading governed by value of the stress intensity factor $K_I$ are given by [2]
\begin{aligned} \sigma_r & =\frac{K_I}{4 \sqrt{2 \pi r}}\left(5 \cos \frac{\theta}{2}-\cos \frac{3 \theta}{2}\right) \ \sigma_\theta & =\frac{K_I}{4 \sqrt{2 \pi r}}\left(3 \cos \frac{\theta}{2}+\cos \frac{3 \theta}{2}\right) \ \sigma_{r \theta} & =\frac{K_I}{4 \sqrt{2 \pi r}}\left(\sin \frac{\theta}{2}+\sin \frac{3 \theta}{2}\right) \end{aligned}
where $r$ is the distance from the origin of the coordinate system placed at the crack tip and $\theta$ is the polar angle.

When the applied loads are not normal to the crack plane mixed-mode conditions apply in the vicinity of the crack tip. The singular stresses in polar coordinates are given in terms of the opening-mode $K_I$ and sliding-mode $K_{I I}$ stress intensity factors by the following equations [2]
\begin{aligned} \sigma_r & =\frac{K_I}{4 \sqrt{2 \pi r}}\left(5 \cos \frac{\theta}{2}-\cos \frac{3 \theta}{2}\right)+\frac{K_{I I}}{4 \sqrt{2 \pi r}}\left(-5 \sin \frac{\theta}{2}+3 \sin \frac{3 \theta}{2}\right) \ \sigma_\theta & =\frac{K_I}{4 \sqrt{2 \pi r}}\left(3 \cos \frac{\theta}{2}+\cos \frac{3 \theta}{2}\right)+\frac{K_{I I}}{4 \sqrt{2 \pi r}}\left(-3 \sin \frac{\theta}{2}-3 \sin \frac{3 \theta}{2}\right) \end{aligned} $$\sigma_{r \theta}=\frac{K_I}{4 \sqrt{2 \pi r}}\left(\sin \frac{\theta}{2}+\sin \frac{3 \theta}{2}\right)+\frac{K_{I I}}{4 \sqrt{2 \pi r}}\left(\cos \frac{\theta}{2}+3 \cos \frac{3 \theta}{2}\right)$$
The sum of the stresses $\sigma_r$ and $\sigma_\theta$ is given by
$$\sigma_r+\sigma_\theta=\frac{2 K_I}{\sqrt{2 \pi r}} \cos \frac{\theta}{2}-\frac{2 K_{I I}}{\sqrt{2 \pi r}} \sin \frac{\theta}{2}$$
Working as in the previous case of opening-mode loading, we obtain the following equations of the caustic
\begin{aligned} & W_x=x^{\prime}=r_0\left[\cos \theta+\frac{2}{3}\left(1+\mu^2\right)^{-1 / 2} \cos \frac{3 \theta}{2}-\frac{2}{3} \mu\left(1+\mu^2\right)^{-1 / 2} \sin \frac{3 \theta}{2}\right] \ & W_y=y^{\prime}=r_0\left[\sin \theta+\frac{2}{3}\left(1+\mu^2\right)^{-1 / 2} \sin \frac{3 \theta}{2}+\frac{2}{3} \mu\left(1+\mu^2\right)^{-1 / 2} \cos \frac{3 \theta}{2}\right] \end{aligned}
With
$$r=r_0=\left(\frac{3 z_0 d c K_I}{2 \sqrt{2 \pi}}\right)^{2 / 5}\left(1+\mu^2\right)^{1 / 5}, \quad \mu=K_{I I} / K_I$$
The stress intensity factors $K_I$ and $K_{I I}$ are obtained as
$$K_I=\frac{1.671}{z_0 d c m^{3 / 2}}\left(\frac{D}{\delta}\right)^{5 / 2} \frac{1}{\sqrt{1+\mu^2}}, \quad K_{I I}=\mu K_I$$
The ratio $D / \delta$ takes either of the values $r_0=D_t / \delta_t, D_l^{\max } / \delta_l^{\max }, D_l^{\min } / \delta_l^{\min }$, where $D_l^{\max }$ and $D_l^{\min }$ are the maximum and minimum diameters of the caustic along the cräck planee and $D_t$ is the transverse (perpendiculär to the crack plané) dianeter of the caustic at the crack tip. The quantities $\delta_l^{\max }$ and $\delta_l^{\min }$ depend on the value of 4. For opening-mode loading $\delta_t=3.16, \delta_l^{\max }=\delta_l^{\min }=3$. Figure 6.13 presents the geometrical construction of the caustic for $\mu=0.5$. In Fig. 6.14 four caustics corresponding to $\mu=0,0.25,1.0$ and $\infty$ are shown. The values of $\mu=0$ and $\infty$ refer to the cases of pure tension (opening-mode loading) and pure shear (sliding-mode loading), respectively. Note that the caustic for $\mu=0$ is symmetric with respect to the $x$-axis, while the other caustics for $\mu \neq 0$ do not present a symmetry. Figure 6.15 presents the variation of the quantities $\delta_t=D_t / r_0, \delta_l^{\max }=D_l^{\max } / r_0, \delta_l^{\min }=D_l^{\min } / r_0$ versus $\mu$. Note that for $\mu=0 . \delta_t=3.16$, while for $\mu=1, \delta_t=2.99$. The variation of the ratio $\left(D_l^{\max }-D_l^{\min }\right) / D_l^{\max }$ versus $\mu$ is shown in Fig. 6.16.

## 力学代考

$$W_x=x-z_0 \frac{\partial(\Delta s)}{\partial x} \quad W_y=y-z_0 \frac{\partial(\Delta s)}{\partial y}$$

$$\sigma_r=\frac{K_I}{4 \sqrt{2 \pi r}}\left(5 \cos \frac{\theta}{2}-\cos \frac{3 \theta}{2}\right) \sigma_\theta=\frac{K_I}{4 \sqrt{2 \pi r}}\left(3 \cos \frac{\theta}{2}+\cos \frac{3 \theta}{2}\right) \sigma_{r \theta}=\frac{K_I}{4 \sqrt{2 \pi r}}(\sin$$

$$\begin{gathered} \sigma_r=\frac{K_I}{4 \sqrt{2 \pi r}}\left(5 \cos \frac{\theta}{2}-\cos \frac{3 \theta}{2}\right)+\frac{K_{I I}}{4 \sqrt{2 \pi r}}\left(-5 \sin \frac{\theta}{2}+3 \sin \frac{3 \theta}{2}\right) \sigma_\theta=\frac{K_I}{4 \sqrt{2 \pi r}}(3 \cos \ \sigma_{r \theta}=\frac{K_I}{4 \sqrt{2 \pi r}}\left(\sin \frac{\theta}{2}+\sin \frac{3 \theta}{2}\right)+\frac{K_{I I}}{4 \sqrt{2 \pi r}}\left(\cos \frac{\theta}{2}+3 \cos \frac{3 \theta}{2}\right) \end{gathered}$$

$$\sigma_r+\sigma_\theta=\frac{2 K_I}{\sqrt{2 \pi r}} \cos \frac{\theta}{2}-\frac{2 K_{I I}}{\sqrt{2 \pi r}} \sin \frac{\theta}{2}$$

$$W_x=x^{\prime}=r_0\left[\cos \theta+\frac{2}{3}\left(1+\mu^2\right)^{-1 / 2} \cos \frac{3 \theta}{2}-\frac{2}{3} \mu\left(1+\mu^2\right)^{-1 / 2} \sin \frac{3 \theta}{2}\right] \quad W_y=y^{\prime}=r_0$$

$$r=r_0=\left(\frac{3 z_0 d c K_I}{2 \sqrt{2 \pi}}\right)^{2 / 5}\left(1+\mu^2\right)^{1 / 5}, \quad \mu=K_{I I} / K_I$$

$$K_I=\frac{1.671}{z_0 d c m^{3 / 2}}\left(\frac{D}{\delta}\right)^{5 / 2} \frac{1}{\sqrt{1+\mu^2}}, \quad K_{I I}=\mu K_I$$

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。

## 物理代写|力学代写mechanics代考|MECH3410

statistics-lab™ 为您的留学生涯保驾护航 在代写力学mechanics方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写力学mechanics代写方面经验极为丰富，各种代写力学mechanics相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• Advanced Probability Theory 高等概率论
• Advanced Mathematical Statistics 高等数理统计学
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 物理代写|力学代写mechanics代考|Mathematical Analysis of Moiré Fringes

Consider two indexed families of curves representing the specimen and reference gratings expressed by the indicial equations
$$S(x, y)=k, R(x, y)=l(k, l=\pm 1, \pm 2, \ldots)$$
When the two gratings are superposed the resulting moiré pattern is expressed by an indexed family of curves $M(x, y)=m(m=\pm 1, \pm 2, \ldots)$. The moiré fringes are the diagonals of the curvilinear quadrangles formed by the intersection of the curves of the two gratings. They are expressed by the following indicial equation (Fig. 3.5).
$$k \pm l=m$$
Points $E, F, G, H, \ldots$ of Fig. $3.5$ correspond to the moiré pattern for which $(k$ $-l)=$ constant, while points $A, B, C, D, \ldots$ of Fig. $3.5$ correspond to the moiré pattern for which $(k+l)=$ constant. The moiré fringes for which the equation $(k-l)$ $=m$ applies is called the subtractive moirépattern, while the moiré fringes for which the equation $(k+l)=m$ applies is called the additive moirépattern. As we mentioned previously, the effective or visible moiré pattern is the pattern with the longest intefringe spacing or the shortest diagonals of the individual quadrangles. The effective moire pattern in Fig. $3.5$ is the pattern containing the fringe $E F G H$ and belongs to the subtractive moiré pattern.

Equation (3.7) indicates that the moiré pattern is the result of adding or subtracting two functions that are expressed parametrically. The moiré pattern can also be considered as a family of parametric curves. Knowledge of any two of the three families of curves allows the determination of the third. In displacement analysis, one family is the master grating and a second is the moiré fringes. The third family is the deformed specimen grating from which the displacements of the specimen are measured.
The effective moiré pattern may change from subtractive type to additive type and vice versa. The boundary between the two moire types is the region in which the individual quadrangles are squares. It is called commutation moiré boundary or simply moiré boundary.

## 物理代写|力学代写mechanics代考|Relationships Between Line Grating and Moiré Fringes

Line gratings are mostly used in experimental mechanics. In this section, we will develop the relationships between the pitches and relative inclination of two lines gratings and the spacing and inclination of the resulting moiré fringes. The moiré fringes are straight lines that coincide with the diagonals of the rhombuses formed by the intersections of the lines of the two gratings. We will use the general method presented previously known as geometric approach.

Consider two lines gratings $S(x, y)=k$ and $R(x, y)=l$ of pitches, $p$ and $p_1=p(1$ $+\lambda$ ), respectively, referred to a system of Cartesian coordinates $O x y$ (Fig. 3.7). The lines of the grating $S(x, y)$ are parallel to the $x$-axis, while the lines of the grating $R(x$, $y$ ) make an angle $\theta$ with the $x$-axis. The line $k=0$ of grating $S(x, y)$ and the line $l=$ 0 of grating $R(x, y)$ pass through the origin $O$ of the system $O x y$.
The equations of the two gratings are expressed by
$$\begin{gathered} S(x, y)=k=\frac{y}{p} \ R(x, y)=1=\frac{y \cos \theta-x \sin \theta}{p(1+\lambda)} \end{gathered}$$

From Eq. (3.7) we obtain for the equation of the fringes of the subtractive moiré pattern
$$\frac{y}{p}-\frac{y \cos \theta-x \sin \theta}{p(1+\lambda)}=m$$
or after rearranging the terms
$$y\left[\frac{\cos \theta-(1+\lambda)}{\sin \theta}\right]+\frac{m p(1+\lambda)}{\sin \theta}=x$$
The moiré fringes are straight lines with an angle of inclination $\varphi$ with the $x$-axis and at a distance $f$ (interfringe spacing) between them. Their equation can also be obtained from Eq. (3.19) by replacing $\theta$ with $\varphi$, and $p(1+\lambda)$ with $f$. We obtain
$$y \cot \varphi-\frac{m f}{\sin \varphi}=x$$

## 物理代写|力学代写mechanics代考|Mathematical Analysis of Moiré Fringes

$$S(x, y)=k, R(x, y)=l(k, l=\pm 1, \pm 2, \ldots)$$

$$k \pm l=m$$

$(k+l)=m$ 应用称为加性莫尔图案。正如我们之前提到的，有效或可见的莫尔图案是具有最长的干涉条纹间距 或各个四边形的最短对角线的图案。图 1 中的有效云纹图案 $3.5$ 是包含条纹的图案 $E F G H$ 属于减法莫尔纹。

## 物理代写|力学代写mechanics代考|Relationships Between Line Grating and Moiré Fringes

$$S(x, y)=k=\frac{y}{p} R(x, y)=1=\frac{y \cos \theta-x \sin \theta}{p(1+\lambda)}$$

$$\frac{y}{p}-\frac{y \cos \theta-x \sin \theta}{p(1+\lambda)}=m$$

$$y\left[\frac{\cos \theta-(1+\lambda)}{\sin \theta}\right]+\frac{m p(1+\lambda)}{\sin \theta}=x$$

$$y \cot \varphi-\frac{m f}{\sin \varphi}=x$$

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。

## 物理代写|力学代写mechanics代考|CIVL2210

statistics-lab™ 为您的留学生涯保驾护航 在代写力学mechanics方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写力学mechanics代写方面经验极为丰富，各种代写力学mechanics相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• Advanced Probability Theory 高等概率论
• Advanced Mathematical Statistics 高等数理统计学
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 物理代写|力学代写mechanics代考|Terminology

The moiré phenomenon occurs whenever a repetitive structure, such as a mess, is overlaid with another such structure. The two structures need not be identical. The effect is observed in everyday life. Examples include the pattern seen through two rows of a mesh, or picket fence from a distance, layers of window screens, or coarse textiles. Before studying the moiré effect we will define a few terms that are needed for its understanding.

The basic element in the moire method is the grating. It consists of equidistant opaque bars of constant width separated by transparent slits. The bars are usually straight lines, even though other forms of lines are used, like circular, radial, etc. The width of the opaque bars is usually equal to the width of the transparent slits.

In some cases, the widths are different producing desirable results. The ensemble is made of an opaque bar and its adjacent transparent slit is termed ruling or line of the grating. The distance between corresponding points of two successive bars or slits is termed pitch and is usually denoted by $p$. The number of rulings per unit length is called spatial frequency of density of the grating. Gratings are characterized by their density. In geometric moiré, the density of the grating cannot exceed 40 lines per $\mathrm{mm}$. For higher density gratings diffraction effects enter and a different approach for the interpretation of the obtained optical pattern is needed. The above gratings that consist of periodic dark lines are called amplitude gratings. There are gratings that transmit light over their whole surface and change the phase of the transmitted light by a periodic variation in thickness or refraction index. They are called phase gratings. Some gratings have the combined characteristics of phase and amplitude gratings. Both types of gratings when combined with another grating produce the moiré effect. In this chapter, we will use only amplitude gratings.

The direction perpendicular to the rulings of a grating is termed principal direction, while the direction parallel to the rulings is called secondary direction. Superposed gratings form successive bright and dark bands, called moiré fringes. The distance between two successive fringes is termed interfringe spacing and is denoted by $f$.

In moiré analysis of strain, two gratings are usually used. One, attached to the specimen, referred to as model or specimen grating, and another superposed to the specimen grating referred to as master or reference grating. Moiré fringes are produced from the superposition of the two gratings. The rulings of the gratings can be regarded as indexed families of curves. Let $S(x, y)=k$ denotes the family of curves corresponding to the specimen grating and $R(x, y)=l$ the family of curves corresponding to the reference grating. $k$ and $l$ are indexing parameters running over a subset of real integers $(0, \pm 1, \pm 2, \ldots)$. Their values define the spacing of the rulings of the gratings.

## 物理代写|力学代写mechanics代考|The Moiré Phenomenon

Consider two line gratings of the same pitch with equal width of opaque bars and transparent slits printed on transparent sheets. Superpose the gratings so that their principal directions coincide (Fig. 3.1). When light passes through the gratings a uniform light or uniform dark field is observed, depending on whether the opaque bars of one grating coincide exactly with the opaque bars of the other grating or weather the opaque bars of one grating coincide exactly with the transparent slits of the other grating, respectively. If one grating is displaced with respect to the other so that the principal directions of the two gratings coincide a uniform field of alternate light and dark bands appear whenever the movement of one grating with respect to the other is half a pitch. Between the light and dark bands, an intermediate gray field of continuously varying intensity appears. The intensity of light behind two superimposed gratings of the same pitch whose dark bars coincide is shown in Fig. 3.2. The eye blends the optical effect and sees uniform average light. The transmitted light intensity behind the gratings is $50 \%$ of the incident intensity. It is assumed that the frequency of the gratings is low (lower than 40 lines per mm) to exclude diffraction effects. The light and dark bands that occupy the whole field as one grating moves relative to the other grating are called moiré fringes. Note that when the two line gratings are moved along the secondary direction (parallel to their lines) no optical effect is produced.

The above observations can be summarized as: Whenever two line grating of the same pitch are displaced one with respect to the other along their principal directions and remain parallel alternate bright and dark fringes appear when the relative movement of one grating with respect to the other equals one pitch. No optical effect is produced when the gratings move in their secondary direction and remain parallel (the direction normal to the grating lines is called principal direction because when the gratings are moved in this direction an optical (moiré) effect is produced, while the direction parallel to the grating lines is called secondary direction because when the gratings are moved in this direction no optical effect is produced). This is the very essence of the moiré phenomenon.
The relative motion $v$ of the two gratings is given by
$$v=n p$$
where $n$ is the number of bright or dark cycles and $p$ is the pitch of the gratings. Equation (3.1) constitutes the fundamental equation of the moiré phenomenon. Small displacements of one pitch are magnified by their transformation into moiré fringes.
From the above analysis, it is clear that the geometric moiré effect is produced by obstruction of light. It does not involve interference or diffraction effects.

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。

## 物理代写|力学代写mechanics代考|FNEG1004

statistics-lab™ 为您的留学生涯保驾护航 在代写力学mechanics方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写力学mechanics代写方面经验极为丰富，各种代写力学mechanics相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• Advanced Probability Theory 高等概率论
• Advanced Mathematical Statistics 高等数理统计学
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 物理代写|力学代写mechanics代考|Diffraction by a Circular Aperture

The diffraction pattern formed by a uniformly illuminated circular aperture consists of a bright central region surrounded by a series of concentric bright and dark rings. It is known as the Airy disk, in honor of Sir George Airy (1801-1892) who first derived the expression for the intensity in the pattern. Figure $2.34$ presents the intensity of light across the diffraction pattern of a circular hole. The pattern is described by the angular radii of the rings. The angle $\theta_1$ that the line from the center of the aperture to the first dark ring makes with the normal to the plane of the pattern is given by
$$\sin \theta_1 \approx \theta_1=1.22 \frac{\lambda}{D}$$
where $D$ is the aperture diameter and $\lambda$ is the wavelength. Note that this formula differs from that of a slit (Eq. (2.43) with $m=1$ ) by the factor $1.22$. This is due to the non-uniform width of the circular slit, as compared to the uniform width of the rectangular slit. It can be shown that the “average” width of a circle of diameter $D$ is $1.22 D$
The angular radii $\theta_2$ and $\theta_3$ of the next two dark rings are given by
$$\sin \theta_2=2.23 \frac{\lambda}{D}, \quad \sin \theta_3=3.24 \frac{\lambda}{D}$$
The angular radii of the bright rings between the dark rings are given by
$$\sin \theta=1.63 \frac{\lambda}{D}, 2.68 \frac{\lambda}{D}, 3.70 \frac{\lambda}{D}$$

## 物理代写|力学代写mechanics代考|Limit of Resolution

When two point objects are very close the diffraction patterns of their images will overlap. As the two objects move closer it is not distinguishable if there are two overlapping images or a single image. The images of two point objects are resolved (they are distinguishable) when they are seen as separate. The minimum separation of two objects that can be resolved by an optical system is the limit of resolution of the optical system. Diffraction effects limit the resolution of a system. A generally accepted criterion for resolution of two objects is the Rayleigh criterion, according to which, two images are resolved when the center of the Airy disk of one image coincides with the first dark ring of the other (Fig. 2.35). The limit of resolution of an optical system is given by Eq. (2.55). The smaller the limit of resolution, the greater the resolving power of an optical system. The limit of resolution of the human eye for most people is $5 \times 10^{-4} \mathrm{rad}$. The limit of resolution of the Hubble telescope for visible light with $\lambda=550 \mathrm{~nm}$ is of the order of $3 \times 10^{-7} \mathrm{rad}$.

It can be shown that in the Fraunhofer diffraction the far field on the image plane is the Fourier transform of spatial signals (grating, lens) in an aperture. Hence, light passing through an aperture will produce the Fourier transform of the aperture plane. Given a function of transparency, its Fourier transform gives the image of transparency. In some cases, for the Fraunhofer approximation to be valid the distance from the aperture to the image plane may be very large, beyond the limits of the laboratory. In order to bring the image to laboratory dimensions, we use a lens. For this reason, the lens is considered a Fourier transform device. We should emphasize that it is not the lens that is the Fourier transforming devise. It is the aperture with or without a lens. The lens makes it possible to make the transform within the dimensions of the laboratory. The transform will be visible at the focal plane of the lens. The lens as a Fourier transforming device is extensively used in optical methods of experimental mechanics.

As an application consider the case of a grating whose amplitude transmittance varies sinusoidally for normal incidence of light. Since the grating has one harmonic, its Fourier transform will produce, besides the zeroth order, the $+1$ and $-1$ orders that deviate from the zeroth order. Thus, a sinusoidal amplitude transmission grating produces two diffracted beams. If the grating is not a sinusoidal one, its amplitude can be considered as a series of sinusoidal terms, and its Fourier transform will produce two inclined diffraction orders for each sinusoidal component of the grating. When the grating transmittance consists of two sine waves, the diffracted pattern will contain four inclined diffraction orders of $\pm 1$, and $\pm 2$.

## 物理代写|力学代写mechanics代考|Diffraction by a Circular Aperture

$$\sin \theta_1 \approx \theta_1=1.22 \frac{\lambda}{D}$$

$$\sin \theta_2=2.23 \frac{\lambda}{D}, \quad \sin \theta_3=3.24 \frac{\lambda}{D}$$

$$\sin \theta=1.63 \frac{\lambda}{D}, 2.68 \frac{\lambda}{D}, 3.70 \frac{\lambda}{D}$$

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。

## 物理代写|力学代写mechanics代考|ENGR20004

statistics-lab™ 为您的留学生涯保驾护航 在代写力学mechanics方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写力学mechanics代写方面经验极为丰富，各种代写力学mechanics相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• Advanced Probability Theory 高等概率论
• Advanced Mathematical Statistics 高等数理统计学
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 物理代写|力学代写mechanics代考|The Wheatstone Bridge

The Wheatstone bridge is an electrical circuit that is employed to measure an unknown electrical resistance. In our case, it is used to measure the change of the resistance a strain gage undergoes when it is subjected to strain. It consists of a constant voltage source, $E_{i}$, four resistors $R_{1}, R_{2}, R_{3}$, and $R_{4}$ arranged in a bridge configuration (Fig. 1.5), and a readout circuit.

We will relate the output voltage $E_{0}$ to the input voltage of the bridge $E_{i}$ using Kirchhoff’s circuit laws. Consider the bridge $A B C D$ (Fig. 1.5). The voltage drop $V_{A B}$ $\operatorname{across} R_{1}$ is
$$V_{A B}=\frac{R_{1}}{R_{1}+R_{2}} E_{i}$$

Similarly, the voltage drop $V_{A D}$ across $R_{4}$ is
$$V_{A D}=\frac{R_{4}}{R_{3}+R_{4}} E_{i}$$
The output voltage $E_{0}$ from the bridge is
$$E_{0}=V_{B D}=V_{A B}-V_{A D}=\frac{R_{1} R_{3}-R_{2} R_{4}}{\left(R_{1}+R_{2}\right)\left(R_{3}+R_{4}\right)} E_{i}$$

## 物理代写|力学代写mechanics代考|Strain Gage Rosettes

The state of strain at a point is defined by the three strain components $\varepsilon_{x x}, \varepsilon_{y y}$, and $\gamma_{x y}$ in a Cartesian system $O_{x y}$. The principal strains $\varepsilon_{1}$ and $\varepsilon_{2}$ and the principal angle $\beta$ are determined by
\begin{aligned} \varepsilon_{1} &=\frac{1}{2}\left(\varepsilon_{x x}+\varepsilon_{y y}\right)+\frac{1}{2} \sqrt{\left(\varepsilon_{x x}-\varepsilon_{y y}\right)^{2}+\gamma_{x y}^{2}} \ \varepsilon_{2} &=\frac{1}{2}\left(\varepsilon_{x x}+\varepsilon_{y y}\right)-\frac{1}{2} \sqrt{\left(\varepsilon_{x x}-\varepsilon_{y y}\right)^{2}+\gamma_{x y}^{2}} \ 2 \beta &=\tan ^{-1} \frac{\gamma_{x y}}{\varepsilon_{x x}-\varepsilon_{y y}} \end{aligned}
Normal strains are measured by strain gages along a certain direction. The strains $\varepsilon_{A}, \varepsilon_{B}$, and $\varepsilon_{C}$ along the directions $A, B$, and $C$ that makes angle $\beta_{A}, \beta_{B}$, and $\beta_{C}$ with the $x$-axis (Fig. 1.6) are given by
\begin{aligned} &\varepsilon_{A}=\varepsilon_{x x} \cos ^{2} \beta_{A}+\varepsilon_{x x} \sin ^{2} \beta_{A}+\gamma_{x y} \sin \beta_{A} \cos \beta_{A} \ &\varepsilon_{B}=\varepsilon_{x x} \cos ^{2} \beta_{B}+\varepsilon_{x x} \sin ^{2} \beta_{B}+\gamma_{x y} \sin \beta_{B} \cos \beta_{B} \ &\varepsilon_{A}=\varepsilon_{x x} \cos ^{2} \beta_{C}+\varepsilon_{x x} \sin ^{2} \beta_{C}+\gamma_{x y} \sin \beta_{C} \cos \beta_{C} \end{aligned}
For the determination of the state of strain at a point measurement of three normal strains along three different directions is needed. Strain gage rosettes with three gages along prescribed directions are used for this purpose. The most common rosettes are the three-element tee (Fig. 1.7a), the rectangular (Fig. 1.7b), and the delta (Fig. 1.7c) rosette.

## 物理代写|力学代写mechanics代考|The Wheatstone Bridge

$$V_{A B}=\frac{R_{1}}{R_{1}+R_{2}} E_{i}$$

$$V_{A D}=\frac{R_{4}}{R_{3}+R_{4}} E_{i}$$

$$E_{0}=V_{B D}=V_{A B}-V_{A D}=\frac{R_{1} R_{3}-R_{2} R_{4}}{\left(R_{1}+R_{2}\right)\left(R_{3}+R_{4}\right)} E_{i}$$

## 物理代写|力学代写mechanics代考|Strain Gage Rosettes

$$\varepsilon_{1}=\frac{1}{2}\left(\varepsilon_{x x}+\varepsilon_{y y}\right)+\frac{1}{2} \sqrt{\left(\varepsilon_{x x}-\varepsilon_{y y}\right)^{2}+\gamma_{x y}^{2}} \varepsilon_{2} \quad=\frac{1}{2}\left(\varepsilon_{x x}+\varepsilon_{y y}\right)-\frac{1}{2} \sqrt{\left(\varepsilon_{x x}-\varepsilon_{y y}\right)^{2}+\gamma_{x y}^{2}} 2 \beta=$$

$$\varepsilon_{A}=\varepsilon_{x x} \cos ^{2} \beta_{A}+\varepsilon_{x x} \sin ^{2} \beta_{A}+\gamma_{x y} \sin \beta_{A} \cos \beta_{A} \quad \varepsilon_{B}=\varepsilon_{x x} \cos ^{2} \beta_{B}+\varepsilon_{x x} \sin ^{2} \beta_{B}+\gamma_{x y} \sin \beta_{B}$$

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。

## 物理代写|力学代写mechanics代考|AUR50216

statistics-lab™ 为您的留学生涯保驾护航 在代写力学mechanics方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写力学mechanics代写方面经验极为丰富，各种代写力学mechanics相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• Advanced Probability Theory 高等概率论
• Advanced Mathematical Statistics 高等数理统计学
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 物理代写|力学代写mechanics代考|Transverse Sensitivity and Gage Factor

The strain sensitivity of a strain gage along its axis $S_{A}$ was defined by Eq. (1.10). Generally, the state of strain at the point of interest is not uniaxial along the axis of the gage but biaxial. It is dictated by the values of the normal strains along the axis of the gage and the transverse direction and the shear strain. The sensing gage is sensitive not only to the axial strain along the axial segments of the strain gage grid pattern but also to the other two strains, the transverse and the shear. These strains are transferred to the sensing gage through the adhesive and the gage carrier material. The response of the gage to the shear strain is small and it can be omitted. Transverse strain sensitivity refers to the response of the gage to strains that are perpendicular to the axis of the gage. The ideal situation is that of strain gages that are completely insensitive to transverse strain. This is the case of plane wire strain gages. The transverse sensitivity of these gages is because a portion of the wire in the end loop lies in the transverse direction. This is not the case for foil strain gages whose transverse sensitivity arises from the grid design and gage construction in a complex manner.

A strain gage has two gage factors as determined in a uniaxial strain field with the gage axes aligned parallel and perpendicular to the strain field. The change of the resistance of the gage, $\Delta R$, per initial resistance, $R$, may be written as
$$\frac{\Delta R}{R}=S_{a} \varepsilon_{a}+S_{t} \varepsilon_{t}$$
where $S_{a}$ is the sensitivity factor of the gage to axial strain, $S_{t}$ is the sensitivity factor to transverse strain, $\varepsilon_{a}$ is the normal strain along the axial direction and $\varepsilon_{t}$ is the normal strain along the transverse direction of the gage. The sensitivity factors $S_{a}$ and $S_{t}$ are dimensionless. Equation (1.18) can be put in the form
$$\frac{\Delta R}{R}=S_{a}\left(\varepsilon_{a}+K_{t} \varepsilon_{t}\right)$$
where $K_{t}=S_{t} / S_{a}$ is the transverse sensitivity factor of the gage.

## 物理代写|力学代写mechanics代考|The Potentiometer Circuit

The potentiometer circuit is shown in Fig. 1.4. It consists of a constant voltage supply, $E_{i}$, the ballast resistor $R_{b}$ and the strain gage resistor $R_{g}$. The output voltage $E_{T}$ is obtained as
$$E_{T}=\frac{R_{g}}{R_{g}+R_{b}} E_{i}=\frac{1}{1+r} E_{i}$$
where $r=R_{b} / R_{g}$.
Let us now consider that the resistances $R_{b}$ and $R_{g}$ change by $\Delta R_{b}$ and $\Delta R_{g}$, respectively, and the output voltage changes by $\Delta E_{T}$. Then, we obtain from Eq. (1.28)
$$E_{T}+\Delta E_{T}=\frac{\left(R_{g}+\Delta R_{g}\right)}{\left(R_{g}+\Delta R_{g}\right)+\left(R_{b}+\Delta R_{b}\right)} E_{i}$$
Equations (1.28) and (1.29) render
$$\Delta E_{T}=\frac{r}{(1+r)^{2}}\left(\frac{\Delta R_{g}}{R_{g}}-\frac{\Delta R_{b}}{R_{b}}\right)(1-\eta) E_{i}$$
where
$$\eta=1-\left[1+\frac{1}{1+r}\left(\frac{\Delta R_{g}}{R_{g}}-r \frac{\Delta R_{b}}{R_{b}}\right)\right]^{-1}$$
With $\Delta R_{b}=0$ and taking into consideration Eq. (1.20), Eq. (1.31) becomes
$$\eta=1-\left[1+\frac{1}{1+r} S_{g} \varepsilon\right]^{-1}$$
Equation (1.32) can be put in the form $\eta=x-x^{2}+x^{3}-x^{4}+\ldots, \quad|x|=\left|\frac{s_{g} \varepsilon}{1+r}\right|<1$

## 物理代写|力学代写mechanics代考|Transverse Sensitivity and Gage Factor

$$\frac{\Delta R}{R}=S_{a} \varepsilon_{a}+S_{t} \varepsilon_{t}$$

$$\frac{\Delta R}{R}=S_{a}\left(\varepsilon_{a}+K_{t} \varepsilon_{t}\right)$$

## 物理代写|力学代写mechanics代考|The Potentiometer Circuit

$$E_{T}=\frac{R_{g}}{R_{g}+R_{b}} E_{i}=\frac{1}{1+r} E_{i}$$

$$E_{T}+\Delta E_{T}=\frac{\left(R_{g}+\Delta R_{g}\right)}{\left(R_{g}+\Delta R_{g}\right)+\left(R_{b}+\Delta R_{b}\right)} E_{i}$$

$$\Delta E_{T}=\frac{r}{(1+r)^{2}}\left(\frac{\Delta R_{g}}{R_{g}}-\frac{\Delta R_{b}}{R_{b}}\right)(1-\eta) E_{i}$$

$$\eta=1-\left[1+\frac{1}{1+r}\left(\frac{\Delta R_{g}}{R_{g}}-r \frac{\Delta R_{b}}{R_{b}}\right)\right]^{-1}$$

$$\eta=1-\left[1+\frac{1}{1+r} S_{g} \varepsilon\right]^{-1}$$

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。

## 物理代写|力学代写mechanics代考|ENSC2004

statistics-lab™ 为您的留学生涯保驾护航 在代写力学mechanics方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写力学mechanics代写方面经验极为丰富，各种代写力学mechanics相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• Advanced Probability Theory 高等概率论
• Advanced Mathematical Statistics 高等数理统计学
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 物理代写|力学代写mechanics代考|Basic Principles

We will develop a relation between the change of resistance of a wire and the strain applied to the wire. From this relation, we will be able to determine the strain by measuring the change of resistance.

Consider a conductor of uniform cross section $A$ (in $\mathrm{mm}^{2}$ ) and length $L$ (in $\mathrm{m}$ ) with specific resistance $\rho$ (defined for $1 \mathrm{~m}$ length, $1 \mathrm{~mm}^{2}$ cross section at $20^{\circ} \mathrm{C}$ ). The electrical resistance $R$ (in Ohms, $\Omega$ ) of the conductor is given by
$$R=\rho \frac{L}{A}$$
Let the resistance of the conductor change by $\mathrm{d} R$, the specific resistance by $\mathrm{d} \rho$ and the cross section area by $\mathrm{d} A$ when the length of the wire changes by $\mathrm{d} L$. Differentiating Eq. (1.1) we obtain $$\mathrm{d} R=\frac{L}{A} \mathrm{~d} \rho+\frac{\rho}{A} \mathrm{~d} L-\frac{\rho L \mathrm{~d} A}{A^{2}}$$
From Eqs. (1.1) and (1.2) we obtain
$$\frac{\mathrm{d} R}{R}=\frac{\mathrm{d} \rho}{\rho}+\frac{\mathrm{d} L}{L}-\frac{\mathrm{d} A}{A}$$
Let calculate the change of the cross section area $\mathrm{d} A$. If $V$ is the volume of the conductor we have
$$V=A L$$
The change of volume $\mathrm{d} V$ when the conductor is stretched is
$$d V=A d L+L d A=V_{f}-V=L_{f} A_{t}-A L$$
where $L, A$, and $V$ are the length, area, and volume before stretching, and $L_{f}, A_{f}$, and $V_{f}$ are the corresponding quantities after stretching of the conductor.

## 物理代写|力学代写mechanics代考|Bonded Resistance Strain Gages

In principle, a single small length of wire bonded on the surface of the component under investigation can serve as a gage to measure the strain at a point. Circuit requirements set a lower limit of approximately $100 \Omega$ on the gage resistance. A gage made of the finest wire with such resistance is about $100 \mathrm{~mm}$ long. In order to reduce the length of the gage the wire is formed into grid type and is bonded to the specimen with adhesives.

Today, metal foil electrical resistance strain gage sensors are most often used in applications. A typical foil strain gage is shown schematically in Fig. 1.2. The conductor with meander shape is printed or etched on the gage carrier material. The strain sensitive pattern is oriented along the direction of stain measuring. The strain gage consists of a sensing element attached to a thin film. The purpose of the film is to serve as an insulator and carrier of the sensing element. The strain gage is bonded on the surface under consideration by an adhesive. The strain to be measured is transferred from the deformed material to the strain gage through the adhesive.

## 物理代写|力学代写mechanics代考|Basic Principles

$$R=\rho \frac{L}{A}$$

$$\mathrm{d} R=\frac{L}{A} \mathrm{~d} \rho+\frac{\rho}{A} \mathrm{~d} L-\frac{\rho L \mathrm{~d} A}{A^{2}}$$

$$\frac{\mathrm{d} R}{R}=\frac{\mathrm{d} \rho}{\rho}+\frac{\mathrm{d} L}{L}-\frac{\mathrm{d} A}{A}$$

$$V=A L$$

$$d V=A d L+L d A=V_{f}-V=L_{f} A_{t}-A L$$

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。

## 物理代写|力学代写mechanics代考|EGR 210

statistics-lab™ 为您的留学生涯保驾护航 在代写力学 mechanics方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写力学 mechanics代写方面经验极为丰富，各种代写力学 mechanics相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• Advanced Probability Theory 高等概率论
• Advanced Mathematical Statistics 高等数理统计学
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 物理代写|力学代写mechanics代考|Stress and Strain

In Chapter 1 we defined stress and strain states at any point within the solid body as having six distinctive components, i.e. three normal and three shear components, with respect to an arbitrary coordinate system. The values of these six components at the given point will change with the rotation of the original coordinate system. It is therefore important to understand how to perform stress or strain transformations between two coordinate systems, and to be able to determine the magnitudes and orientations of stress or strain components that result. One key reason for stress or strain transformation is that the strains are normally measured in the laboratory along particular directions, and they must be transformed into a new coordinate system before the relevant stresses can be re-calculated. In this chapter we discuss the stress/strain transformation principles and the key role they play in the stress calculation of a drilled well at any point of interest; whether vertical, horizontal or inclined.

## 物理代写|力学代写mechanics代考|TRANSFORMATION PRINCIPLES

Let’s consider the cube of Figure 1.2, and cut it in an arbitrary way such that the remaining part will form a tetrahedron. The reason for choosing a tetrahedron for this analysis is that a shape with four sides has the least number of planes to enclose a point. Figure $2.1$ shows the stresses acting on the side and cut planes of the tetrahedron. The stress acting on the cut plane is denoted by $S$, which can be resolved into three components along the respective coordinate axes, assuming $n$ defines the directional normal to the cut plane.

Assuming the cut plane to have an area of unity, i.e. $A=1$, the areas of the remaining cube sides can be expressed as (Figure 2.2):
\begin{aligned} &A=1 \ &A_{1}=\cos (n, y) \ &A_{2}=\cos (n, x) \ &A_{3}=\cos (n, z) \end{aligned}

## 物理代写|力学代写mechanics代考|TRANSFORMATION PRINCIPLES

$$A=1 \quad A_{1}=\cos (n, y) A_{2}=\cos (n, x) \quad A_{3}=\cos (n, z)$$

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。

## 英国补考|力学代写mechanics代考|CRN 33240

statistics-lab™ 为您的留学生涯保驾护航 在代写力学 mechanics方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写力学 mechanics代写方面经验极为丰富，各种代写力学 mechanics相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• Advanced Probability Theory 高等概率论
• Advanced Mathematical Statistics 高等数理统计学
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 英国补考|力学代写mechanics代考|STRESS COMPONENTS

We start with a general three-dimensional case as shown in Figure 1.3. This figure shows a cube with the respective stresses. Only the stresses acting on the faces of the cube are shown. Balance of forces requires that equal stresses act in the opposite direction on each of the three sides of the cube.

Nine different components of stress can be seen in Figure 1.3. These are required to determine the state of stress at a point. The stress compo nents can be grouped into two categories; $\sigma_{x}, \sigma_{\gamma}$ and $\sigma_{z}$ as normal stresses, and, $\tau_{x y}, \tau_{y x}, \tau_{x z}, \tau_{z x}, \tau_{y z}$ and $\tau_{z y}$ as shear stresses.

The stress components have indices, which relate to the Cartesian coordinate system. The first index defines the axis normal to the plane on which the stress acts. The second index defines the direction of the stress component. Normal stresses with two identical indexes are given with one index, e.g. $\sigma_{x x} \equiv \sigma_{x}$.

## 英国补考|力学代写mechanics代考|DEFINITION OF STRAIN

When a body is subjected to loading it will undergo displacement and/or deformation. This means that any point in/on the body will be shifted to another position. Deformation is normally quantified in terms of the original dimension and it is represented by strain, which is a dimensionless parameter. Strain is therefore defined as deformation divided by the original or non-deformed dimension and is simply expressed by:
$$\varepsilon=\frac{\Delta l}{l_{o}}$$
where $\varepsilon$ is the strain, $\Delta l$ is the deformed dimension (measured in $\mathrm{m}$ or in) and $l_{\mathrm{o}}$ is the initial dimension (measured in $\mathrm{m}$ or in).

Strains are categorized as engineering strain and scientific strain. While the initial/original dimension is used throughout the analysis in the engineering strain, in scientific strain, the actual dimension, which changes with time, is applied.

Equation $1.4$ is derived by using the concept of small deformation theory. If large deformations are involved, Equation $1.4$ is no longer valid, and other definitions are required. Two main large deformation formulas are introduced by Almansi and Green. These are expressed by:
$$\varepsilon=\frac{P-P_{o}}{2 l^{2}}$$ known as Almansi strain formula, and:
$$\varepsilon=\frac{l^{2}-l_{o}^{2}}{2 l_{o}^{2}}$$
known as Green strain formula, respectively. It can be shown that for small deformations Equations $1.5$ and $1.6$ will be simplified to Equation 1.4. The error of using Equation $1.3$ may be negligible for many cases compared to other assumptions.

## 英国补考|力学代写mechanics代考|DEFINITION OF STRAIN

$$\varepsilon=\frac{\Delta l}{l_{o}}$$

$$\varepsilon=\frac{P-P_{o}}{2 l^{2}}$$

$$\varepsilon=\frac{l^{2}-l_{o}^{2}}{2 l_{o}^{2}}$$

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。