# 统计代写|主成分分析代写Principal Component Analysis代考|Exercises and Problems in Finite Element Analysis of Structures

This text presents a series of exercises and problems that progressively develop the understanding and application of the finite element method for analyzing structures. The problems range from basic static force equilibrium calculations to advanced finite element analysis of trusses with varying geometries, loads, and boundary conditions. Below is a brief summary of each exercise:

3.1: This problem asks to solve a two-member truss using equilibrium equations to find forces in members and reaction forces, then calculates axial deflections and node displacements given member stiffness.

3.2: This problem repeats the previous calculation but uses the finite element approach instead to compare results.

3.3 & 3.4: These exercises involve verifying a matrix transformation equation and demonstrating singularity of a transformed stiffness matrix.

3.5 & 3.6: These tasks ask to calculate the stiffness matrix for various bar elements in global coordinates considering different geometries and units.

3.7 & 3.8: For multiple truss structures, students are asked to create element-to-global displacement correspondence tables and express connectivity data in matrix form.

3.9: Given global displacements, calculate element-level quantities like axial displacements, strains, stresses, and nodal forces, comparing the stress with the formula F/A.

3.10 & 3.11: For two separate truss structures, the objective is to find node deflections, axial stress in each element, and assemble the global stiffness matrix using the direct stiffness method.

3.12: This problem is a variation of Problem 3.11, asking to redo the analysis after removing certain elements.

3.13: Analyze a cantilever truss under specified conditions to find global displacements, axial stress, reaction forces, and check equilibrium.

3.14 & 3.15: These exercises deal with a truss supported by a linear spring and require calculating global displacements, reaction forces, checking equilibrium and energy balance, repeating the process without the spring.

3.16: Investigate the effect of a horizontal movement in one node on the overall solution for the truss in Problem 3.13.

3.17 & 3.18: These are algebraic systems of equations requiring rearrangement and solving for unknowns using a partitioned matrix approach.

3.19: Solve for the global displacement components at node 3 and stress in each element for a given truss structure.

3.20: Calculate the global stiffness matrix for 3-D truss elements with given material properties and nodal coordinates.

3.21: Directly verify a specific matrix equation.

3.22: Demonstrate that the axial stress formula in a 3-D truss element reduces to the 2-D case.

3.23: Find axial stress and nodal forces for elements in a 3-D truss under given displacement conditions.

3.24 & 3.25: Express the strain energy of a bar element in terms of global displacements and apply Castigliano’s theorem or the principle of minimum potential energy to derive the global stiffness matrix.

3.26: Assemble the global stiffness matrix for a 3-D truss and compute node displacements and element stresses.

These problems provide a comprehensive set of practice exercises to learn and apply the finite element method to analyze structures ranging from simple 2-D trusses to complex 3-D configurations.

### 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。