# 统计代写|主成分分析代写Principal Component Analysis代考|Finite Element Analysis of a 2D Truss Structure

This passage describes a detailed finite element analysis of a two-dimensional truss structure depicted in Figure 3.6a. It walks through the sequential steps involved in the analysis to determine displacements, reaction forces, strains, and stresses:

System Definition: The global coordinate system is established, nodes are numbered, and element connectivity is defined.

Element Stiffness Computation: Individual element stiffness values are calculated based on material properties, geometry, and orientation angles.

Transformation to Global Coordinates: The element stiffness matrices are transformed to align with the global coordinate system.

Assembly Preparation: Two methods are described to construct the element-to-global displacement correspondence: a tabular representation and an element-node connectivity table.

Global Stiffness Matrix Assembly: The global stiffness matrix is built by adding up the contributions from each element stiffness matrix based on their connectivity.

Application of Boundary Conditions: Nodes 1 and 2 are fixed, so their displacements are set to zero, and the relevant rows and columns of the global stiffness matrix are eliminated to create the reduced system of equations for the “active” displacements.

Solution for Unconstrained Displacements: The remaining system of equations is solved numerically to find the displacements at the unconstrained nodes.

Calculation of Reaction Forces: The reaction forces at the constrained nodes are computed by substituting the obtained displacements back into the original global equilibrium equations.

Determination of Strain and Stress: For each element, the local displacements are computed using the global displacements and element orientations. These are then used to calculate the axial strain and stress within each element. An example computation is provided for element 2.

Verification and Presentation of Results: Results for all eight elements are summarized in a table, showing that the finite element analysis was performed using different software tools (spreadsheet, MATLAB, and commercial FE software) and yielded consistent results. Positive stress values indicate tension, and negative values represent compression.

Overall, this example demonstrates the systematic and structured approach used in finite element analysis to solve engineering problems involving structural mechanics.

### MATLAB代写

MATLAB 是一款高性能的技术计算语言，集成了计算、可视化和编程环境于一体，以熟悉的数学符号表达问题和解决方案。MATLAB 的基本数据元素是一个不需要维度的数组，使得能够快速解决带有矩阵和向量公式的多种技术计算问题，相比使用 C 或 Fortran 等标量非交互式语言编写的程序，效率大大提高。MATLAB 名称源自“矩阵实验室”（Matrix Laboratory）。最初开发 MATLAB 的目标是为了提供对 LINPACK 和 EISPACK 项目的矩阵软件的便捷访问，这两个项目代表了当时矩阵计算软件的先进技术。经过长期发展和众多用户的贡献，MATLAB 已成为数学、工程和科学入门及高级课程的标准教学工具，在工业界，MATLAB 是高效研究、开发和分析的理想选择。MATLAB 提供了一系列名为工具箱的特定应用解决方案集，这对广大 MATLAB 用户至关重要，因为它们极大地扩展了 MATLAB 环境，使其能够解决特定类别问题。工具箱包含了针对特定应用领域的 MATLAB 函数（M 文件），涵盖信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等诸多领域。