Study on derivation and optimization algorithm about thin plate bending large deformation higher-order nonlinear partial differential equations

Abstract

For a thin plate bending large deformation problem, variational principle is applied, and higher-order nonlinear partial differential equations about thin plate bending large deformation is established. Based on difference method and dynamic design variable optimization method, making unknown deflection of discrete coordinate points as design variables, differential equations sets of the discrete coordinates points as building objective function, a dynamic design variable optimization algorithm for computing thin plate bending deflection is proposed. Universal computing program is designed. Practical example about rectangular thin plate with fixed boundary under uniform load is analyzed. Comparing the program computing result with finite element solution. Effectiveness and feasibility of the method are verified. This method can be used to solve engineering problem.