基于B可微方程组的弹塑性动力接触问题的研究  

INVESTIGATION ON ELASTOPLASTIC DYNAMIC CONTACT PROBLEMS BASED ON B-DIFFERENTIABLE EQUATIONS

作　　者：高航舵 胡志强[1,2] 尹昭 林皋[1,2] GAO Hang-duo;HU Zhi-qiang;YIN Zhao;LIN Gao(State Key Laboratory of Coastal and Offshore Engineering,Dalian University of Technology,Dalian 116024,China;School of Hydraulic Engineering,Faculty of Infrastructure Engineering,Dalian University of Technology,Dalian 116024,China)

机构地区：[1]海岸与近海工程国家重点实验室,大连理工大学,大连116024 [2]工程抗震研究所,建设工程学部水利工程学院,大连理工大学,大连116024

出　　处：《工程力学》2025年第2期24-32,共9页Engineering Mechanics

基　　金：国家自然科学基金项目(52209157)。

摘　　要：该文基于B可微方程组法,提出了一种求解弹塑性动力摩擦接触问题的算法。将接触条件表示成B可微方程组的形式,可精确满足库仑-摩擦条件;将接触求解嵌套在本构方程的求解过程中,可有效减少接触柔度阵由于刚度阵的变化而引起的更新次数,从而节省计算时间;采用带一维Armijo型线搜索的阻尼Newton-Raphson法保证了接触方程在迭代过程中的数值收敛性。在算例部分,通过与基于增广拉格朗日算法的ANSYS的结果对比,验证了所提出算法的准确性,并利用一个工程实例验证了该方法的实用性与鲁棒性。A novel method based on B-differentiable equations is proposed to solve the elastoplastic dynamic contact problems with friction.The contact conditions are expressed in the form of B-differentiable equations,which can exactly satisfy Coulomb’s law of friction.By nesting the contact solution in the iterative process of constitutive equations,the number of solutions for contact flexibility matrix,which changes with stiffness matrix,is reduced significantly,further resulting in a shorter computational time.In addition,the damped Newton-Raphson method with 1D Armijo type linear search is applied in the solution of contact equations,which provides a good numerical convergence.Through a comparison with the commercial software ANSYS,the accuracy of the proposed algorithm is verified in two numerical examples,and the practicality and robustness of the method are supported in an engineering example.

关 键 词：固体力学 结构分析 B可微方程组法 摩擦接触问题 弹塑性问题 

分 类 号：O313.5[理学—一般力学与力学基础] O344.3[理学—力学]