单层网壳结构弹塑性屈曲分析的离散单元法研究

该文提出离散元塑性区法，即将任意2个球元的接触截面划分成若干小面积，通过各小面积的应力状态描述整个截面的塑性发展过程，较离散元塑性铰法更精确。该文推导了杆系离散元截面应变增量计算公式，建立了截面在三维应力-应变状态下的结构弹塑性本构方程、加卸载准则、截面内力积分公式以及计算分析流程。离散元弹塑性屈曲分析的追踪策略与弹性屈曲分析完全相同，即仍采用离散元力控制法或位移控制法。采用Fortran语言自编程序对若干单层网壳结构算例进行弹塑性屈曲分析，验证了离散元塑性区法的正确性和适用性，拓宽了离散单元法在工程领域的应用范围，为结构分析提供了新路径。

DISCRETE ELEMENT METHOD FOR ELASTOPLASTIC BUCKLING ANALYSIS OF SINGLE-LAYER RETICULATED SHELLS

This paper presents a discrete element plastic zone method which could be recognized as an exact solution compared with the discrete element plastic hinge method.In the method,the contact cross section between two arbitrary adjacent particles is divided into a finite number of monitored subsections,while the spread of plasticity over the cross section is captured by tracing the stress state of each subsection.The incremental section strain formula in the member Discrete Element Method(DEM)is derived first,then the space elastoplastic constitutive equation,the loading and unloading criterion as well as the integral formula of section internal force are established in turn.Either discrete element force control method or the displacement control method for tracing elastic buckling behavior can be employed directly in elastoplastic buckling analysis.Finally,the calculation flowchart of elastoplastic buckling analysis process in DEM is obtained and an object-oriented computer program is compiled by Fortran Language.The computer program is used to investigate the elastoplastic buckling behaviors of several single-layer reticulated shells.The comparisons made have verified the correctness and applicability of the proposed discrete element plastic zone method.Additionally,the application range of DEM in structural engineering is extended and a novel approach for structural analysis is provided.