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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|固体力学代写Solid Mechanics代考|DEVIATORIC STRESS

When stresses are developed in non-rigid body, dilation and distortion occur. In relation to that, the developed stresses are divided into two components for the convenience of analysis: hydrostatic stress, which is responsible for dilation and deviatoric stress, which is responsible for distortion.

Hydrostatic stress is the average of three principal stresses along the respective axes and acting along all three axes. Deviatoric stress is the difference between principal stress and hydrostatic stress along all three axes. Consider a body develops different amount of stresses along three mutually orthogonal axes. Different strains, which are hydrostatic strain and deviatoric strain corresponding to their counterparts, are shown. It can be observed that when deviatoric stress along an axis is high, the distortion of body along that axis is significant, as indicated in Fig. 2.18.
The hydrostatic stress can be written as follows:
$$\sigma_m=\frac{\sigma_x+\sigma_y+\sigma_z}{3} .$$
Applying the relationship in Eq. (2.35) to the equation above yields the following expression:
$$\sigma_m=\frac{I_1}{3} .$$
Dilation due to hydrostatic stress is the uniform displacement of particles across a solid, whether it is towards or away from each other. In contrast, distortion due to deviatoric stress is differential displacement of particles across the solid. Therefore, distortion in this case is very likely to break the bond between particles compared to dilation. In other words, deviatoric stress is the kind of stress responsible for yielding. It is essential for engineers and material scientists when the plastic behaviour of solid is concerned.

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

An octahedral plane inclines equally against three mutually orthogonal axes. It is possible to form eight octahedral planes and an octahedron as a result, as shown in Fig. 2.19.

Consider an octahedral plane $A B C$ below. As an octahedral plane, the lengths $O A, O B$ and $O C$ are equal, as shown in Fig. 2.20.
Applying the relationship in Eq. (2.12) into Eq. (2.13) yields the following
$$1=\left(\frac{x}{r}\right)^2+\left(\frac{y}{r}\right)^2+\left(\frac{z}{r}\right)^2$$
Simplification of the equation to express $r$ in terms of the orthogonal axes gives us the following expression:
$$r^2=x^2+y^2+z^2 .$$
$x, y$ and $z$ represent $O C, O B$ and $O A$, respectively, and $O A=O B=O C$, therefore, the above equation can be written as:
$$r^2=O A^2+O A^2+O A^2 .$$
Simplifying the equation above results in the following:
\begin{aligned} &r^2=3 O A^2 \ &r=\pm \sqrt{3} O A \end{aligned}
By applying the definition of $r$ as per Eq. (2.49) and $x=O A$ into Eq.

# 固体力学代考

## 物理代写|固体力学代写Solid Mechanics代考|偏应力

$$\sigma_m=\frac{\sigma_x+\sigma_y+\sigma_z}{3} .$$

$$\sigma_m=\frac{I_1}{3} .$$

## 物理代写|固体力学代写Solid Mechanics代考|八面体应力

$$1=\left(\frac{x}{r}\right)^2+\left(\frac{y}{r}\right)^2+\left(\frac{z}{r}\right)^2$$

$$r^2=x^2+y^2+z^2 .$$
$x, y$ 和 $z$ 代表 $O C, O B$ 和 $O A$，和 $O A=O B=O C$，因此，上式可写成:
$$r^2=O A^2+O A^2+O A^2 .$$
.
.
\begin{aligned} &r^2=3 O A^2 \ &r=\pm \sqrt{3} O A \end{aligned}的定义 $r$ 根据式(2.49)和 $x=O A$ 进入Eq.

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## 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。

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