# 统计代写|主成分分析代写Principal Component Analysis代考|Interpolation Functions and Continuity in Finite Element Analysis

The structural elements introduced in the previous chapters were formulated on the basis of known principles from elementary strength of materials theory. We have also shown, by example, how Galerkin’s method can be applied to a heat conduction problem. This chapter examines the requirements for interpolation functions in terms of solution accuracy and convergence of a finite element analysis to the exact solution of a general field problem. Interpolation functions for various common element shapes in one, two, and three dimensions are developed, and these functions are used to formulate finite element equations for various types of physical problems in the remainder of the text. With the exception of the beam element, all the interpolation functions discussed in this chapter are applicable to finite elements used to obtain solutions to problems that are said to be C0 -continuous. This terminology means that, across element boundaries, only the zeroth-order derivatives of the field variable (i.e., the field variable itself) are continuous. On the other hand, the beam element formulation is such that the element exhibits C1 -continuity, since the first derivative of the transverse displacement (i.e., slope) is continuous across element boundaries, as discussed previously and repeated later for emphasis. In general, in a problem having Cn -continuity, derivatives of the field variable up to and including nth-order derivatives are continuous across element boundaries.

### 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。