Interface reduced substructuring using polynomials for non-smooth line-like interfaces

Abstract

A method for reducing the interface degrees of freedom on a substructure by means of polynomial basis vectors is developed for interfaces composed of distinct edges and corners. The scope is restricted to interfaces with straight line geometry. Two sets of polynomials are utilized to enforce compatibility at corners where two edges meet. The first set accounts for motion at the corners and are referred to as corner polynomials, and the second accounts for higher frequency motion allowing each edge to move independently of the others, referred to as edge polynomials. Due to the interface motion being described by an identical set of basis vectors on adjacent substructures, coupling along interfaces with incompatible meshes is possible without significant loss in the accuracy of dynamic properties of the assembly. This interface reduction technique is discussed in the framework of creating an assembly from copies of a parent substructure, in which the parent substructure has reduced internal and interface degrees of freedom and is then translated and rotated into a larger assembly. The reduced basis is demonstrated on several plate substructures, and shown to provide accurate estimates of the assembly’s dynamic properties. This accuracy increases proportionally with the number of basis vectors used to describe the interface motion, but can deteriorate if the order of the basis polynomials chosen cannot be resolved by the interface mesh.