A HYSTERETIC FORMULATION FOR ISOGEOMETRIC ANALYSIS AND SHAPE OPTIMIZATION OF PLANE STRESS STRUCTURES

Abstract. In this work, a new hysteretic formulation for the inelastic static and dynamic analysis of plane stress problems within the framework of Isogeometric Analysis (IGA) is presented. The Bouc-Wen model is utilized as a smooth hysteretic, rate independent model, capable of expressing the hysteretic behaviour that can be easily extended to account for stiffness degradation, strength deterioration and pinching phenomena. On the basis of the classical theory of plasticity, the generalized 3D Bouc-Wen model is expressed in tensorial form incorporating the yield criterion and linear or nonlinear, isotropic or kinematic hardening law. Subsequently, basis functions generated from Non-Uniform Rational B-Splines (NURBS) and the appropriate control points define the structure’s geometry and are employed to build the elastic stiffness matrix. Then, the elastic formulation is extended by considering as additional hysteretic degrees of freedom the plastic strains at the quadrature points defined by the appropriate quadrature rule for the numerical integration. The evolution of the plastic strains is determined by a Bouc–Wen evolution equation and the solution provides the displacements at control points of the structure and the plastic strains at the quadrature points. On the basis of the proposed formulation the shape optimization problem is formulated using mathematical programming. The objective function is the minimum mass of the structure and the control points of the boundary and/or the control weights are selected as the optimization design variables. Furthermore, stress and displacement constraints are imposed at specific points. Finally, numerical results are presented that validate the proposed hysteretic formulation. A good agreement is achieved between the standard FEM and the proposed scheme.