A 3D Constrained Optimization Smoother to Post-process Quadrilateral Meshes for Body-in-white

Abstract

Finite element analyses of 3D quadrilateral meshes for automotive body-in-white panels have stringent mesh quality requirements. Several mesh quality metrics, namely element included angles, minimum Jacobian determinant, skew, taper, warp, aspect ratio, minimum element length etc. need to be within acceptable limits. No constitutive relations exist that can tie all these parameters to a single metric that mesh post-processing can target. In the paper presented, a 3D optimization smoothing algorithm is proposed based on element included angles with the constraints of a minimum edge length and geometry fidelity envelope. A complex cost-function is set up for each element based on included element angle at the element corners. Element angle perturbation methods are devised to exercise local control on included angles of quadrilateral and mixed meshes. A minimization principle is worked out to reduce the cost function to an acceptable limit. Goal proximity is defined by acceptable error norms and ranges. Mesh nodes are repositioned iteratively but bound by a geometry fidelity envelope apart from the minimum element edge length constraint. Striking improvement in mesh quality statistics is reported with reasonably monotonic solution convergence patterns.