A user-defined finite element for laminated glass panels and photovoltaic modules based on a layer-wise theory

Laminated plates with glass skin layers and a core layer from polyvinyl butyral are widely used in the civil engineering and automotive industry. Crystalline or thin film photovoltaic modules are composed from front and back glass or polymer layers and a solar cell layer embedded in a polymeric encapsulant. For the structural analysis of such laminates, layer-wise theories (LWTs) for plates have been introduced in literature. In this paper, an extended LWT is proposed to assure the C0 continuity. Based on this theory, a finite element formulation and a user-defined quadrilateral serendipity element with quadratic shape functions and nine degrees of freedom (DOFs) is presented. The element is implemented using the Abaqus subroutine “User Element”. Benchmark problems are developed to examine the accuracy and efficiency of the proposed element for a wide range of material properties including the limiting cases of shear compliant and shear rigid laminates. An emphasis is placed on the influence of boundary conditions with respect to additional degrees of freedom as well as on accurate representation of boundary layer effects.