## 物理代写|固体力学代写Solid Mechanics代考|MCHE4380

statistics-lab™ 为您的留学生涯保驾护航 在代写固体力学Solid 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。我们的专家在代写固体力学Solid Mechanics代写方面经验极为丰富，各种代写固体力学Solid Mechanics相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (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|固体力学代写Solid Mechanics代考|STRESS EQUILIBRIUM EQUATION

Stresses is a continuous function of the location in a body. Therefore, the stress at any point is interrelated with the stress at other points. When force is acting along the $x$-axis of a solid, normal stress $\sigma_x$ is developed at the contacting surface.

The solid is a continuum and internal force is exerted by the contacting particles on the others. As a result, stress develops in the entire solid body rather than just the contacting point. Considering the rate of stress development per unit length along $x$-axis as $\frac{\partial \sigma_x}{\partial x}$, the increment in stress across the length $d x$ is:
$$\Delta \sigma_x=\frac{\partial \sigma_x}{\partial x} d x$$
If the point on solid is at rest and in equilibrium, the stress developed along the $x$ axis due to the aforementioned external force and internal force will be balanced by a stress of the same magnitude but in a different direction. Therefore, $\sigma_x^{\prime}$ can be expressed in term of $\sigma_x$ :
$$\sigma_x^{\prime}=\sigma_x+\frac{\partial \sigma_x}{\partial x} d x$$
Similarly, the following normal stress components can be defined based on Eq. (2.4):
\begin{aligned} &\sigma_y^{\prime}=\sigma_y+\frac{\partial \sigma_y}{\partial y} d y \ &\sigma_z^{\prime}=\sigma_z+\frac{\partial \sigma_z}{\partial z} d z \end{aligned}
Six shear stress components can be expressed in a similar fashion:

\begin{aligned} &\tau_{x y}^{\prime}=\tau_{x y}+\frac{\partial \tau_{x y}}{\partial x} d x \tau_{y x}^{\prime}=\tau_{y x}+\frac{\partial \tau_{y x}}{\partial y} d y \ &\tau_{x z}^{\prime}=\tau_{x z}+\frac{\partial \tau_{x z}}{\partial x} d x \tau_{z x}^{\prime}=\tau_{z x}+\frac{\partial \tau_{z x}}{\partial z} d z \ &\tau_{y z}^{\prime}=\tau_{y z}+\frac{\partial \tau_{y z}}{\partial y} d y \tau_{z y}^{\prime}=\tau_{z y}+\frac{\partial \tau_{z y}}{\partial z} d z \end{aligned}
A total of 18 stress components can be expressed in the above-derived forms. All these unknown stress components can now be determined by knowing only nine of them, as shown in Table $2.2$.

## 物理代写|固体力学代写Solid Mechanics代考|STRESS TRANSFORMATIONS

In real-life applications, force does not always act parallel to any of the global axes. To ease analysis, it can be expressed in terms of direction cosine after being divided into three components, along each of the global $x, y$ and $z$ directions.

After analysis, stresses and strains along global axes are determined. Using direction cosine, the stresses and strains can be changed into a resultant stress and strain that is inclined in all three axes. The plane that has this resultant stress as its normal is known as the oblique plane. The inclination of the oblique plane can be expressed in direction cosine as well.

Sometimes, rather than just referring to the global axes for every case, another set of mutually orthogonal axes can be defined by transforming the global axes with a particular inclination. This approach is usually used when there is no force exerted or developed along previously defined global axes. Such transformation requires least effort when the body is isotropic, where its mechanical properties are not dependent on its orientation, as shown in Fig. 2.9.

Consider a general 3-D vector, $r$, across three mutually orthogonal axes. Let $\alpha$ be the inclination angle between the vector and $x$-axis, $\beta$ be the inclination angle between the vector and $y$-axis and $\gamma$ be the inclination angle between the vector and z-axis, as shown in Fig. 2.10.
The trigonometric relationships between $x, y, z$ and $r$ are:
\begin{aligned} &\cos \alpha=\frac{x}{r}=l \ &\cos \beta=\frac{y}{r}=m \ &\cos \gamma=\frac{z}{r}=n \end{aligned}
By applying the Pythagoras theorem, vector $r$ can be expressed as:
$$r^2=x^2+y^2+z^2$$

## 物理代写|固体力学代写Solid Mechanics代考|应力平衡方程

.

$$\Delta \sigma_x=\frac{\partial \sigma_x}{\partial x} d x$$

$$\sigma_x^{\prime}=\sigma_x+\frac{\partial \sigma_x}{\partial x} d x$$

\begin{aligned} &\sigma_y^{\prime}=\sigma_y+\frac{\partial \sigma_y}{\partial y} d y \ &\sigma_z^{\prime}=\sigma_z+\frac{\partial \sigma_z}{\partial z} d z \end{aligned}
6个剪应力分量可以用类似的方式表示:< /p>

\begin{aligned} &\tau_{x y}^{\prime}=\tau_{x y}+\frac{\partial \tau_{x y}}{\partial x} d x \tau_{y x}^{\prime}=\tau_{y x}+\frac{\partial \tau_{y x}}{\partial y} d y \ &\tau_{x z}^{\prime}=\tau_{x z}+\frac{\partial \tau_{x z}}{\partial x} d x \tau_{z x}^{\prime}=\tau_{z x}+\frac{\partial \tau_{z x}}{\partial z} d z \ &\tau_{y z}^{\prime}=\tau_{y z}+\frac{\partial \tau_{y z}}{\partial y} d y \tau_{z y}^{\prime}=\tau_{z y}+\frac{\partial \tau_{z y}}{\partial z} d z \end{aligned}

## 物理代写|固体力学代写Solid Mechanics代考|应力转换

\begin{aligned} &\cos \alpha=\frac{x}{r}=l \ &\cos \beta=\frac{y}{r}=m \ &\cos \gamma=\frac{z}{r}=n \end{aligned}

$$r^2=x^2+y^2+z^2$$

## 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。

## 物理代写|固体力学代写Solid Mechanics代考|ENGS33

statistics-lab™ 为您的留学生涯保驾护航 在代写固体力学Solid 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。我们的专家在代写固体力学Solid Mechanics代写方面经验极为丰富，各种代写固体力学Solid Mechanics相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (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|固体力学代写Solid Mechanics代考|FORCE AND STRESS

Force can be described as two distinctive actions: push and pull. A body reacts to exerted force by changing its velocity based on the force’s magnitude and direction. According to Newton’s third law of motion, for every unit of force exerted by one body on another, an equal magnitude of force will be exerted back to it in the opposite direction. Take a restrained girder, as shown in Fig. 2.1, as an example, where supports 1 and 2 are, in fact, two bodies in contact with the girder.

When force is exerted on the girder, it is transmitted throughout the body. When the force is transferred to the point of contact with any of the restrain, Newton’s third law of motion will come into play and a reaction force will be exerted by the support to the girder.

Force is transmitted throughout the body via particles. At the microscopic level, particles will change their velocity from zero (at rest) to a certain value. The moving particles will fill the void between them and because of the attraction force, the nearby particles are pushed or pulled as well. In short, particles will experience an internally developed force in every direction.

By cutting the solid and inspecting the sectional plane, one can find such internal forces acting on that plane. The concept of stress, which is the average of the resultant internal forces distributed over that sectional plane, is introduced.

In engineering, two main types of force are concerned: normal force and shear force. Therefore, normal stress and shear stress are two fundamental types of stress discussed in solid mechanics. Normal stress is developed by a normal force acting perpendicularly to a plane (Fig. 2.2) while shear stress is developed by a shear force acting parallelly to a plane (Fig. 2.3).

## 物理代写|固体力学代写Solid Mechanics代考|COMPONENTS OF STRESS

Solid mechanics studies the stresses and strains at any point on a body, usually illustrated using an infinitesimal cube enveloping the point. Since solids are three dimensional, we can define three mutually orthogonal axes by setting that point as centre. The stress and strain at this point can be categorised based on their direction, with each of them acting along a certain axis. Without other axes to be compared,the defined axes can be assumed not to have any inclination. This will be our reference axes, or global axes, as indicated in Fig. 2.4.

Suppose a force is exerted along the $x$-axis. The developed stress acting along the $x$-axis is distributed over the plane $y z$, which is the plane normal to the $x$-axis. The resultant stress is normal stress along the $x$-axis, $\sigma_x$. Meanwhile, the stress acting along the $y$-axis is distributed over the face of the plane $y z$, which often results in a change in the plane’s shape. The resulting stress is shear stress distributed along the $y$-axis due to the force acting parallelly on the normal plane of the $x$-axis, $\tau_{x y}$. Similarly, $t_{x z}$ is known as the shear stress distributed along the $z$-axis due tô the force acting parallelly on the normal plane of the $x$-axis. The notation for strain components can be interpreted in the same way.

Table $2.1$ shows the generalised stress components on each face in all directions. All 18 unknown stress components need to be solved as all of them are independent of each other.

Shear stress is coupled. Then, by taking the resultant of normal stresses along each axis, the stress at a point is said to be defined completely by nine independent components (three normal and six shear components). The components of stress are as follows:
$$\sigma=\left[\begin{array}{ccc} \sigma_X & \tau_{x y} & \tau_{x z} \ \tau_{y x} & \sigma_Y & \tau_{y z} \ \tau_{z x} & \tau_{z y} & \sigma_Z \end{array}\right]$$
where $\sigma_X=\sigma_x+\sigma_x^{\prime}, \sigma_Y=\sigma_y+\sigma_y^{\prime}$ and $\sigma_Z=\sigma_z+\sigma_z^{\prime}$.

## 物理代写|固体力学代写Solid Mechanics代考|应力的组成

$$\sigma=\left[\begin{array}{ccc} \sigma_X & \tau_{x y} & \tau_{x z} \ \tau_{y x} & \sigma_Y & \tau_{y z} \ \tau_{z x} & \tau_{z y} & \sigma_Z \end{array}\right]$$

## 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|固体力学代写Solid Mechanics代考|EGR210

statistics-lab™ 为您的留学生涯保驾护航 在代写固体力学Solid 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。我们的专家在代写固体力学Solid Mechanics代写方面经验极为丰富，各种代写固体力学Solid Mechanics相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (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|固体力学代写Solid Mechanics代考|Heterogenfous Material

A heterogeneous material shows a distinctive composition at the microscopic level, at any location on it. Since all constituent materials are not evenly distributed over the material, its properties are said to be dependent on the location on the material.
An example for heterogeneous material is reinforced concrete, which is a composite consisting of two main construction materials: concrete and steel.

The dominant constituent material, concrete, shows good compression but poor tension. On the other hand, steel shows good tension, but its strength declines tremendously after being subjected to very high temperature and corrosion.

The combination of concrete and steel, i.e. reinforced concrete, is an economical solution to improving the structural member’s resistance to compression, tension, bending and shear.

For example, when load is applied on the top of a beam, a sagging moment is induced. The top of the beam is subjected to compression, while the bottom is subjected to tension. The primary reinforcing steel bars are placed at the bottom of the beam to help resist the tension. Concrete is casted around the steel bars to hold them in place and provide protection against high temperature and corrosion.

Consider that the tension is applied at two different locations on a reinforced concrete, as shown in Fig. $1.3$ below. Due to the difference in composition at different locations, the material’s behaviour varies at the point that consists of concrete only; the deformation there is significantly higher than that at the point that consists of both concrete and steel.

## 物理代写|固体力学代写Solid Mechanics代考|Homogeneous Material

An ideal homogeneous material shows a uniform composition at the microscopic level, at any location on it. Since all constituent materials are well-distributed over the material, its properties are said to be independent of the location on the material.

An example of a homogeneous material is stainless steel. Its constituent materials are iron ore, chromium, silicon, nickel, carbon, manganese and nitrogen. The first step in manufacturing stainless steel is heating the constituent materials, melting them and letting them mix. The process is important to ensure the final product is homogeneous. Fig. $1.4$ shows the steel manufacturing process as described above.

An anisotropic material shows six different mechanical properties when force is acting in six different directions along three mutually orthogonal axes, i.e. principal axes. In other words, its properties are dependent on the orientation of the material.
A composite is usually anisotropic. It is created by combining two or more constituent materials with different properties. The final material is created by arranging these constituent materials in either a specific or a vnon-specific order without breaking the arrangement of their particles. This makes the final material anisotropic, because the properties of each constituent material are only present throughout the space that such a constituent material occupies.

An example of a composite is fibre-reinforced concrete. In a fibre-reinforced concrete block, concrete provides principal resistance to compression, while fibre, e.g. synthetic fibre. provides principal resistance to tension. Fibre is an anisotropic material. It shows highest resistance to tension only when the force is acting along its longitudinal axis. Therefore, the orientation and arrangement of fibre directly affect the tensile strength of the concrete.

In a fibre-reinforced concrete block, the arrangement and orientation of constituent materials, aggregates, sand, cement (components of concrete) and fibres are always arbitrary in every direction. This causes the tensile strength of fibrereinforced concrete to vary in different directions, as shown in Fig. 1.5.

## 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。