大挠度变截面欧拉梁曲率参数化模型

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中图分类号：TH112

DOI：10.3969/j.issn.1004-132X.2025.08.011 开放科学（资源服务）标识码（OSID）：

Abstract：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 eficiency of large deflection analysis based on curvature approximation. The pro posed approach represented the curvature of deflection curve by Bernstein polynomials. Then the static equilibrum 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 thatthe expression of bending strain energy and stress are simple and accurate，and the generalized stifness matrix is aconstant symmetric square matrix related to the variation of the cross-sectional moment of iner tia.Therefore，both modeling accuracy and computational eficiency 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.

Key words：compliant mechanism；variable cross-section beam；large deflection；parameterization model

0 引言

长细比较大可忽略剪切影响的细长梁一般又称为欧拉梁或欧拉-伯努利梁，它以弯曲变形为主，能实现较大行程且工作应力小，常作为柔顺机构的柔性单元[1]。（剩余15581字）