# 数学代写|有限元方法代写Finite Element Method代考|JEE350

#### Doug I. Jones

Lorem ipsum dolor sit amet, cons the all tetur adiscing elit

couryes™为您提供可以保分的包课服务

couryes-lab™ 为您的留学生涯保驾护航 在代写有限元方法Finite Element Method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。我们的专家在代写有限元方法Finite Element Method代写方面经验极为丰富，各种代写有限元方法Finite Element Method相关的作业也就用不着说。

## 数学代写|有限元方法代写Finite Element Method代考|Deformation and strain

When subjected to external forces, an internal material point located, for example, at position $P$ before the loading, moves to point $P^{\prime}$ as depicted in two dimensions (a two-dimensional solid) in Fig. 2.6. The position of all material points in this solid domain are referred to a fixed Cartesian reference frame, and the position of point $P$ ‘ is found as follows (Fig. 2.6):
$$\vec{r}_{p^{\prime}}=\vec{r}_p+\vec{u}$$
where $\vec{u}$ is the deformation vector. For a general deformation in threedimensional space, the deformation vector is represented as follows:
$$\vec{u}=u_x \hat{i}+u_y \hat{j}+u_z \hat{k}$$
where $u_x, u_y$, and $u_z$ are the projections of $\vec{u}$ onto the $x, y$, and $z$ axes, respectively.

Uniaxial deformation, also referred to as the simple loading, is the type of deformation that can be described with respect to a single orientation (e.g., $x$ ). Typical examples of this type of loading are the elongation/compression of a bar by a tensile/compressive force (Fig. 2.5).

In order to describe the uniaxial deformation in a slender bar, consider an infinitesimally small segment $B C$ of length $d x$ before deformation as shown in Fig. 2.19B. Once the external load is applied in the $x$ direction, the bar deforms. Point $B$ moves to $B$ ‘ where its position change $u$ is described by the deformation vector as follows:
$$\vec{u}=u \hat{i}$$
Note that $u=u(x)$. As the point $B$ moves to the position $B$ ‘, the point $C$ moves to position $C^{\prime}$ and undergoes a position change of $u+(d u / d x) d x$. Thus, the distance between points $C B$ changes from $d x$ to $d x+(d u / d x) d x$.

Elongation/contraction along a given direction is measured by using the normal strain $\varepsilon$ which is defined as the ratio of the change in length along a given direction to the original length as follows:
$$\varepsilon=\frac{1}{d x}\left[\left(1+\frac{d u}{d x}\right) d x-d x\right]=\frac{d u}{d x}$$

## 数学代写|有限元方法代写Finite Element Method代考|Planar deformation

In some problems deformation is confined into a plane. A material point $P$ in the undeformed material will move to point $P^{\prime}$ after deformation as shown in Fig. 2.6. This deformation can be represented by a deformation vector $\vec{u}$. In case of the planar deformation depicted in Fig. 2.6, the deformation vector can be expressed in a Cartesian coordinate system as follows:
$$\vec{u}=u_x \hat{i}+u_y \hat{j}$$
where $u_x$ and $u_y$ are the projections of $\vec{u}$ on the $x$ and $y$ axes, respectively. In vector form, the deformation vector is represented as follows:
$${u}=\left{\begin{array}{ll} u_x & u_y \end{array}\right}^T$$

Note that, in general, the deflection components $u_x$ and $u_y$ vary from point to point inside the deforming solid. Therefore, these variables are functions of the $x$ and $y$ coordinates, $u_x=u_x(x, y)$ and $u_y=u_y(x, y)$.

Deformation of a small rectangle around the point $P$ with side lengths $d x$, $d y$ and unit depth is shown Fig. 2.6. As a result of deformation, point $A$ in the undeformed configuration moves to point $A$ ‘. Similarly points $B, C$, and $D$ move to $B^{\prime}, C^{\prime}$, and $D^{\prime}$.

For the two-dimensional deformation depicted in Fig. 2.6, the original length of the side $A B$ is $d x$. The length of the projection of the deformed line $A^{\prime} B$ ‘ on the $x$ axis is $\left(d x+\left(\partial u_x / \partial x\right) d x\right.$. Thus, by using Eq. (2.36), we can define the normal strain along the $x$ direction as follows:
$$\varepsilon_{x x}=\frac{\partial u_x}{\partial x}$$
It can be similarly shown that the normal strain along the $y$ direction is defined as follows:
$$\varepsilon_{y y}=\frac{\partial u_y}{\partial y}$$

# 有限元方法代考

## 数学代写|有限元方法代写Finite Element Method代考|Deformation and strain

$$\vec{r}_{p^{\prime}}=\vec{r}_p+\vec{u}$$

$$\vec{u}=u_x \hat{i}+u_y \hat{j}+u_z \hat{k}$$

$$\vec{u}=u \hat{i}$$

$$\varepsilon=\frac{1}{d x}\left[\left(1+\frac{d u}{d x}\right) d x-d x\right]=\frac{d u}{d x}$$

## 数学代写|有限元方法代写Finite Element Method代考|Planar deformation

$$\vec{u}=u_x \hat{i}+u_y \hat{j}$$

$${u}=\left{\begin{array}{ll} u_x & u_y \end{array}\right}^T$$

$$\varepsilon_{x x}=\frac{\partial u_x}{\partial x}$$

$$\varepsilon_{y y}=\frac{\partial u_y}{\partial y}$$以上翻译结果来自有道神经网络翻译（YNMT）· 通用场景

## 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。

Days
Hours
Minutes
Seconds

# 15% OFF

## On All Tickets

Don’t hesitate and buy tickets today – All tickets are at a special price until 15.08.2021. Hope to see you there :)