Treffer: A nodal variable method of structural topology optimization based on Shepard interpolant

A method for topology optimization of continuum structures based on nodal density variables and density field mapping technique is investigated. The original discrete-valued topology optimization problem is stated as an optimization problem with continuous design variables by introducing a material density field into the design domain. With the use of the Shepard family of interpolants, this density field is mapped onto the design space defined by a finite number of nodal density variables. The employed interpolation scheme has an explicit form and satisfies range-restricted properties that makes it applicable for physically meaningful density interpolation. Its ability to resolve more complex spatial distribution of the material density within an individual element, as compared with the conventional elementwise design variable approach, actually provides certain regularization to the topology optimization problem. Numerical examples demonstrate the validity and applicability of the proposed formulation and numerical techniques.