Orientation optimization in components fabricated with anisotropic material properties

Abstract

A method for optimizing orientations of an anisotropic material in a component. For example, the method overcomes the non-uniqueness and gimbal locking problems associated with using Euler angles to define the orientation by instead parameterizing the orientation using an orientation tensor that is a self-dyadic product of a direction vector. To avoid non-linear constraints in the mathematical design variables used in the optimization, isoparametric shape functions map the mathematical design variables to physical design variables, and the mapping ensures that various constraints associated with tensor invariants of the orientation tensor are satisfied even though these constraints are not directly imposed on the mathematical design variables. The physical design variables are used to model the component, whereas optimization is performed using the mathematical design variables. Thus, optimization is greatly simplified by removing the tensor-invariant constraints from the optimization step to the mapping step.