Mesh-free energy element method for three-dimensional static analysis of structures with complex geometries

A novel mesh-free numerical method, energy element method (EEM), is proposed for the static analysis of three-dimensional (3D) structures with complex geometries, using global admissible functions, extended interval integrals, Gauss quadrature, and global variable stiffness. This method builds a minimum cuboid that wraps the 3D structure and then cutouts are made to simulate its geometric configuration. To simulate the strain energy of the 3D structure, the cuboid is divided into multiple cuboid energy elements of variable scales based on its geometric configuration. Sufficient Gaussian points are generated in each energy element. Each elastic stiffness coefficient is discretized into a 3D variable stiffness matrix with the same dimensions of Gaussian points in each energy element, where the Gaussian points with zero stiffness are located at the cuboid's cutouts. The construction of the variable stiffness based discrete energy system leads to high-precision numerical simulations of strain energies of 3D structures. Finally, the standard energy functional for 3D structural static analysis is established and solved using the minimum potential energy principle and Ritz method. Static problems of 3D structures such as spheres, perforated plates, and stiffened plates, are investigated. The results are compared with those of the existing literature and finite element method (FEM).