板壳非线性分析的新理论新方法

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。

A NEW THEORY AND A NEW METHOD FOR NONLINEAR ANALYSIS OF PLATES AND SHELLS

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 strainvector increments. These relations are named as increment theory of elastic-plastic strain, increment theory ofthermal elastic-plastic strain, increment theory of elastic-viscoplastic strain and increment theory of thermalelastic-viscoplastic strain, respectively. Consequently, yield surface, loading surface, flow rule and complexnonlinear 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 constitutive relations and finite element methods. It is simple, convenient and rapidly convergent. A unified scheme for nonlinear analysis of plates and shells is established, which is applicable to geometric nonlinear analysis, material nonlinear analysis and double nonlinear analysis.