S型悬臂梁柔度性能的计算与分析

Compliance calculation and analysis for a S-type cantilever beam

基于线弹性和小变形假设理论,以卡氏第二定理为理论基础,推导了S型悬臂梁x向、y向和z向柔度的解析计算公式,利用有限元方法对柔度解析式进行校验。通过定义柔度比函数,比较了倒角S型悬臂梁、直梁S型悬臂梁和圆弧S型悬臂梁的柔度性能。结果表明:S型悬臂梁各柔度计算公式的相对误差均在10%以内,理论分析与仿真结果基本吻合,验证了S型悬臂梁各柔度解析式的正确性。当倒角S型悬臂的γ=0.2时,圆弧S型悬臂梁的x向和z向柔度最大,直梁S型悬臂梁的y向柔度最大。当α=18,β=6时,直梁S型悬臂梁的y向柔度最大,圆弧S型悬臂梁的z向柔度最大;倒角S型悬臂的参数0.2≤γ≤2.2时,圆弧S型悬臂梁的x向柔度最大;倒角S型悬臂的参数γ>2.2时,倒角S型悬臂梁的x向柔度最大。本文的研究内容为S型悬臂梁的工程设计和应用提供了理论基础。

Based on the theory of linear elasticity and small deformation,analytical calculation formulas for compliances in x,y and z directions of a S-type cantilever beam were deduced by using Castigliano’s second theorem.The correctness of these formulas was verified by using the finite element method(FEM).Compliances of curved S-type cantilever beam,straight one and arc one were compared by defining the compliance ratio function.The results showed that relative errors of various compliance calculation formulas for S-type cantilever beams are all less than 10%,theoretical analysis results agree well with simulation ones to verify the correctness of various compliance analytical calculation formulas for S-type cantilever beams;whenγ=0.2 for curved S-type cantilever beam,compliances in x and z directions of arc one are the largest,compliance in y direction of straight one is the largest;whenα=18 andβ=6,compliance in y direction of straight S-type cantilever beam is the largest,and compliance in z direction of arc one is the largest;when 0.2≤γ≤2.2 for curved S-type cantilever beam,compliance in x direction of arc one is the largest;whenγ>2.2 for curved S-type cantilever beam,compliance in x direction of curved one is the largest;the study results provide a theoretical basis for engineering design of S-type cantilever beams and their application.