Deformation Research Of Sandwich Structure Based On Stochastic Finite Element Method

Sandwich structure is gaining wide popularity in shipbuilding and aerospace industry as excellent mechanical properties like high strength-to-weight ratio, high stiffness-to-weitht ratios, designability etc. The complexity and particularity of the sandwich structure cause the randomness of the structure behavior. Traditional finite element method can not fully reflect the response of sandwich structure.In this paper, the local average random discrete units dispersed the local stationary random field, and written program to achieve the corresponding relationship between the finite element grid and the random field grid and caculated the covariance matrix of random variables. The elastic matrixes, the stiffness matrixes and their partial derivative matrixes were derived based Zig-zag sandwich plate finite element model and written corresponding program to calculate the stiffness matrixes and their partial, derivatives matrixes. The perturbation stochastic finite element method and Neumann stochastic finite element method formulation to caculate the deformation of sandwich structures were derived, through computer programs to obtain the first order and second order partial derivative of the response, and further to obtain the statistical characteristics of the response. Comparing with the Monte Carlo results, the result was verified correctly.For a typical sandwich structure, the effect of the random material properties on the structure response was researched, and obtained the statistical characteristics of the response. Case studies include the following: variation of node displacement with clamped boundary; distribution of load, the same coefficient of variation and different boundary conditions; distribution of loads, different coefficient of variation and different boundary conditions; distribution of loads, different coefficient of variation and different core thickness of; the plate of the variation of the response under static load position.The numerical results reveal the influence of random material parameters on the deformation of sandwich structure, and have a certain guiding significance for its optimized design, safety and reliability.