A unified formulation for composite quasi-3D elements based on global–local superposition—part I: element formulation

In a series of two papers, a unified formulation for new plate composite elements is proposed that captures through-the-thickness effects, specifically normal and transverse shear stresses and strains. Thermal effects are also considered, including thermal effects through-the-thickness. This first paper is devoted to the fundamentals of the proposed unified formulation. The elements proposed are displacement based and the number of degrees of freedom is kept as small as possible, all of them possessing clear physical meaning. The elements are built using local functions defined at each layer and global functions defined along the thickness. The consistency of the kinematic assumptions is guaranteed through the imposition of displacement continuity along the thickness direction, transverse stress continuity and boundary conditions at the bottom and top surfaces of the elements. The formulations are developed for either isotropic or orthotropic materials. The formulations shall prove substantially more efficient than those based on solid elements traditionally used to capture normal transverse stresses. In the sequel, a second paper presents a variety of numerical results obtained using the proposed formulation and discusses its capabilities and potential.