The Investigation of a Method to Improve Static Stiffness of Automobile Body Use Eigenvalue Decomposition of the stiffness matrix.

Automobile body design is performed using structural analysis by numerical calculation, but to make it efficient, it is important to establish a technique that can quickly derive the structure satisfying the target value. Although optimization methods are used in many design studies, problems sometimes arise in the actual design stage, and conventional methods in which designers make iterative design changes based on trial and error are still widely used. However, when designing the mutual average compliance defined by the sum of the weights of displacements including displacements other than the external force acting point, it is difficult to derive a design plan because the strain energy, which is a general rigidity index, is not proportional to the mutual average compliance. Furthermore, even if the design sensitivity is calculated, it is difficult for the designer to estimate the type of required stiffness from the sensitivity of the scalar quantity without the displacement shape, as a result, structure examination requires more time. In this paper, we propose a method to reduce the absolute value of mutual average compliance using eigenvalues and eigenmodes obtained by eigenvalue decomposition of the stiffness matrix. First, the eigenvalues and eigenmodes of the stiffness matrix are explained, and the relationship between the mutual mean compliance is clarified. Using a cantilever beam model as an example, it was confirmed that the designer could efficiently carry out the conventional iterative design change by replacing the design problem of mutual average compliance with the design problem of eigenvalues of the stiffness matrix.