Inverse Problems Of Chair Surface Material Elastic Parameter Determination Based On Pressure Comfort

The product design in engineering has become a new research field in Applied Mathematics and Computational Mathematics. Based on the theory of pressure comfort, this thesis studies the inverse problem of elastic parameters determination of chair surface material with respect to hard seat. Traditionally, the seat is designed based on life experiences or scientific experiments without theoretical guidance. This thesis aims at providing a scientific explanation for the seat design by inverse problems approach for elastic parameters determination in the body-seat system.Based on the theory of small deflection of thin plate in elastic mechanics, the thesis establishes a static mechanical model for the body-seat system. Under some reasonable assumptions, the direct problem is formulated by a boundary value problem of partial differential equation of displacement function on the seat surface. The finite integration method is used to discretize the boundary value problem, and the resulted linear algebraic system is solved by regularization method. The error estimates for the displacement distribution on the seat surface are also obtained. The numerical results show that the direct problem can reasonably describe the static elastic mechanical characteristics under small deformation. Compared with other numerical methods, the finite integration method is more suitable for the numerical solution of the direct problem.Aiming at the pressure comfort range of the human hip, we present the mathematical formulation of the inverse problems on the basis of the direct problem. We construct the least squares for the optimal decision of the elastic parameters of the chair surface material and apply the golden section algorithm to solve the least squares problem. Then the optimal solution of the elastic parameters of the chair surface is obtained. To verify the rationality of the inverse problems, the optimal parameters are used to solve the direct problem, and the pressure distribution of the contact surface is obtained to judge comfort level. The research results of the direct problem and the inverse problems provide theoretical support for the optimal selection of the material parameters of the chair surface in the product design.