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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

## 物理代写|力学代写mechanics代考|HOOKE’S LAW

A linear relationship exists between the stress and strain as shown in Figure $4.2 \mathrm{~b}$ and is given by the following equation:
$$\sigma_{x}=E \varepsilon_{x}$$
where:
$$\sigma_{x}=\frac{F_{x}}{A}$$
and the engineering strain definition of $\varepsilon_{x}$, i.e. Equation $1.4$, is used:
$$\varepsilon_{x}=\frac{\Delta l}{l_{o}}$$
Equation $4.1$ is known as Hooke’s law of deformation, and the slope of the stress-strain diagram is referred to as the Modulus of Elasticity (Young’s modulus), $E$.

Using $\sigma_{x}$ and $\varepsilon_{x}$ in Equation 4.1, Hooke’s law can also be expressed as:
$$\Delta l=\frac{F_{x} l_{o}}{E A}$$
The tensor representation of Hooke’s law is given by:
$$\sigma_{i j}=L_{i j k l} \varepsilon_{k l}$$
where all stress and strain components are coupled with anisotropic properties. It should be noted that the simplest possible representation should always be used, as the above equation can be very complex and difficult to solve.

## 物理代写|力学代写mechanics代考|HOOKE’S LAW IN SHEAR

The properties of materials in shear can be evaluated from shear tests or by other methods such as a torsion test. In either method, a plot of shear stress versus shear strain is produced, which is similar to the strain-stress plot that results from a normal tension test (see Figure 4.1). This is known as shear stress-shear strain relation.

From the stress-strain plot, we can determine properties such as the modulus of elasticity, yield strength and ultimate strength. These properties in shear are usually about half the size of similar properties in tension, and they are evaluated using a shear stress-shear strain plot.

For many materials, the initial part of a shear stress-shear strain plot is a straight line, which is the same as the plot that results from a tension test. For this linearly elastic region, the shear stress and shear strain are proportional, and can therefore be expressed in a similar form to Equation $4.1$ as given below:
$$\tau=G \gamma$$
where $\tau$ is the shear stress, $G$ is shear modulus or modulus of rigidity and $\gamma$ is the shear strain.
Equation $4.5$ is the one dimensional Hooke’s law in shear.

# 力学代考

## 物理代写|力学代写mechanics代考|HOOKE’S LAW

$$\sigma_{x}=E \varepsilon_{x}$$

$$\sigma_{x}=\frac{F_{x}}{A}$$

$$\varepsilon_{x}=\frac{\Delta l}{l_{o}}$$

$$\Delta l=\frac{F_{x} l_{o}}{E A}$$

$$\sigma_{i j}=L_{i j k l} \varepsilon_{k l}$$

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assignmentutor™您的专属作业导师
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