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.