### 英国补考|力学代写mechanics代考|CRN 33240

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• 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

## 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 If large deformations are involved, Equation $1.4$ is no longer valid, and other definitions are required.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

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

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

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

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## MATLAB代写

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