The passage discusses the enhancement of the flexure element to include axial loading capabilities, which broadens its application beyond linear beam structures to planar frames. By adding axial stiffness, the element can now handle both axial and transverse loading, allowing it to model structures like frames where joints exhibit bending resistance. When orienting the beam-axial element at an arbitrary angle θ relative to the global reference frame, the element stiffness matrix needs to be transformed accordingly.

The passage presents the 6×6 element stiffness matrix for a flexure element with axial loading and explains that it can be considered as a noncoupled superposition of axial and bending stiffnesses. It further details how to transform the element stiffness matrix and element displacements to the global coordinate system using a transformation matrix [R].

A worked example involves a frame structure with two beam-axial elements subjected to a uniform load. The stiffness matrices for each element are calculated, and one of them undergoes a 90-degree rotation to align with the global coordinate system. The assembled system stiffness matrix and displacement correspondence table are presented, and the system equations are derived.

Upon solving these equations, the displacement values at the unconstrained nodes are obtained. Stress computations for the beam-axial element involve combining bending stresses with direct axial stresses. The bending stresses are computed at the element ends using the curvature formula, and the axial stress is calculated directly from the axial deformation. The maximum stress is identified as the sum of the compressive axial stress and the compressive portion of the bending stress at the appropriate location.

### 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。