Sandwich plates of minimal compliance

• Published in: Computer methods in applied mechanics and engineering Vol. 197; no. 51; pp. 4866 - 4881
• Main Authors: Czarnecki, S., Kursa, M., Lewiński, T.
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier B.V 15.10.2008; Elsevier
• Subjects: Computational techniques; Exact sciences and technology; Fundamental areas of phenomenology (including applications); Mathematical methods in physics; Minimum compliance problem; Physics; Sandwich plates; Solid mechanics; Static elasticity (thermoelasticity...); Structural and continuum mechanics; Topology optimization; Topology optimization; Sandwich plates; Minimum compliance problem; Interfacial layer; Geometrical shape; Sandwich structure; Homogenization; Reissner model; Material selection; Topology; Modeling; Optimization; Optimal design; Plate; Finite element method; Ill posed problem; Hencky model; Effective medium model; Transverse shear
• ISSN: 0045-7825; 1879-2138
• DOI: 10.1016/j.cma.2008.07.005

The subject of the paper is an optimal choice of material parameters characterizing the core layer of sandwich plates within the framework of the conventional plate theory in which the core layer is treated as soft in the in-plane direction. The mathematical description is similar to the Hencky–Reissner model of plates with transverse shear deformation. Here, however, the bending stiffnesses and the transverse shear stiffnesses can be designed independently. The present paper deals only with optimal design of the core layer to make the plate compliance minimal. Two core materials are at our disposal, which leads to the ill-posed problem. To consider it one should relax this problem by admitting composite domains and characterize their overall properties by the homogenization formulae. The numerical approach is based on this relaxed formulation thus making it mesh-independent. The equilibrium problem is solved by the DSG3 finite element method. The optimization results are found with using the convergent updating schemes of the COC method.