An Isogeometric Proportional Topology Optimization Method for Compliance Minimization of Gradient-Elastic Kirchhoff–Love Plates

Abstract

This paper presents an effective isogeometric proportional topology optimization (IPTO) approach for the topology optimization of gradient-elastic thin plates. The structural model is formulated by incorporating Kirchhoff–Love (KL) plate kinematics into the simplified strain-gradient elasticity theory (SSGT). The corresponding weak form requires the third derivatives of the primary kinematic field, i.e., the transverse deflection, which can be efficiently addressed using the nonuniform rational B-spline (NURBS)-based isogeometric analysis (IGA) method. A density-based topology optimization problem for compliance minimization is then formulated, in which the solid isotropic material with penalization (SIMP) method is employed to interpolate the material properties. The material density at each integration point is updated in proportion to its compliance value, which is the key feature that eliminates the need for explicit sensitivity analysis. Subsequently, an element-wise NURBS representation of the material density is constructed and blended to obtain a global NURBS density field over the entire design domain. Selected numerical examples involving both classical elasticity (CE)- and SSGT-based plate problems are presented to demonstrate the accuracy and effectiveness of the presented topology optimization approach.