板壳非线性分析的新理论新方法.docxVIP

第 21 卷第 1 期 工 程 力 学 Vol.21 No.1 2004 年 2 月 ENGINEERING MECHANICS Feb. 2004 文章编号1000-4750(2004)01-0009-06 板壳非线性分析的新理论新方法 秦 荣 (广西大学土木建筑工程学院南宁 530004) 摘 要提出了板壳非线性分析的新理论新方法首先建立了下列几个新的本构关系塑性应变向量增量与总应变向量增量的新关系热塑性应变向量增量与总应变向量增量及温度应变向量增量的新关系粘塑性应变向量增量与总应变向量增量的新关系热粘塑性应变向量增量与总应变向量增量及温度应变向量增量的新关系这些关系分别称为弹塑性应变增量理论热弹塑性应变增量理论弹粘塑性应变增量理论及热弹粘塑性应变增量理论避开了屈服曲面加载曲面流动法则及复杂的非线性应力应变关系其次建立了非线性样条无网格法这种方法是以新的本构关系几何非线性理论变分原理广义变分原理加 权残数法及样条离散化为基础建立的避免了经典本构关系及有限元法带来的巨大困难及缺陷不仅计算简便而且精度高收敛速度很快建立了板壳非线性分析的统一格式对板壳的几何非线性分析材料非线性分析及双重非线性分析都适用 关键词板壳结构非线性新的本构关系样条离散化样条无网格法中图分类号0344 文献标识码A A NEW THEORY AND A NEW METHOD FOR NONLINEAR ANALYSIS OF PLATES AND SHELLS QIN Rong (Civil Engineering Institute, Guangxi University, Nanning 530004, China) Abstract: In this paper, a new theory and a new method for nonlinear analysis of plates and shells are presented. First of all, new constitutive relations are presented, which include new relation of plastic strain vector increment and total strain vector increment, new relation of thermal plastic strain vector increment and total strain and temperature strain vector increments, new relation of viscoplastic strain vector increment and total strain vector increment, new relation of thermal viscoplastic strain vector increment and total strain and temperature strain vector increments. These relations are named as increment theory of elastic-plastic strain, increment theory of thermal elastic-plastic strain, increment theory of elastic-viscoplastic strain and increment theory of thermal elastic-viscoplastic strain, respectively. Consequently, yield surface, loading surface, flow rule and complex nonlinear stress-strain relations are made unnecessary. Next, a spline meshless method for nonlinear analysis is presented. The method is based on new constitutive relations, geometric nonlinear theory, variational principle, generalized variational principle, weighted residual methods and spline partitions. The method overcomes the difficulties and defects of traditional const