摘要
为了实现结构和性能的优化,变截面梁在柔顺机构中愈来愈受到重视,针对其大挠度分析难以兼顾精度和效率的挑战,提出了一种基于曲率逼近的参数化建模方法。采用Bernstein多项式表示挠曲线曲率,基于最小总势能原理建立静力平衡方程,应用高斯积分和牛顿-拉弗森迭代法进行数值求解。其优点是弯曲应变能及应力的计算简单而精确,且广义刚度矩阵是与截面惯性矩变化相关的常值对称方阵,因而建模精度高、数值计算收敛速度快。同时,基于曲率参数解,结果后处理简便快捷。多个算例的数值仿真结果充分证明了所提方法的有效性和优越性。
In order to achieve optimization of structures and performances,variable cross-section beams were increasingly valued in compliant mechanisms.A parametric model was proposed to address the challenge of accuracy and efficiency of large deflection analysis based on curvature approximation.The proposed approach represented the curvature of deflection curve by Bernstein polynomials.Then the static equilibrium equation was established based on the principle of minimum total potential energy,and the numerical solution was obtained via Gaussian quadrature and Newton-Raphson iteration.The advantages are that the expression of bending strain energy and stress are simple and accurate,and the generalized stiffness matrix is a constant symmetric square matrix related to the variation of the cross-sectional moment of inertia.Therefore,both modeling accuracy and computational efficiency are significantly improved.Furthermore,the post-processing is simple and fast based on the solution of curvature parameters.Numerical examples fully demonstrate the effectiveness and superiority of the proposed model.
作者
黄勇刚
谢丹
HUANG Yonggang;XIE Dan(Chongqing Key Laboratory of Green Design and Manufacturing of Intelligent Equipment,ChongqingTechnology and Business University,Chongqing,400067;College of Engineering and Technology,Southwest University,Chongqing,400715)
出处
《中国机械工程》
北大核心
2025年第8期1757-1766,共10页
China Mechanical Engineering
基金
国家自然科学基金(51805448)
中央高校基本科研业务费专项资金(SWU-KT22025)。
关键词
柔顺机构
变截面梁
大挠度
参数化模型
compliant mechanism
variable cross-section beam
large deflection
parameterization model
作者简介
黄勇刚,男,1976年生,副教授、博士。研究方向为机构学与机器人及机械系统CAE。E-mail:hyg@ctbu.edu.cn。;通信作者:谢丹,女,1987年生,讲师、博士。研究方向为计算力学、刚柔耦合多体系统理论及应用。E-mail:danxie2017@swu.edu.cn。
