An automatic approach for the acoustic analysis of three-dimensional bounded and unbounded domains by scaled boundary finite element method

Free vibration and transient dynamic response of functionally graded sandwich plates with power-law nonhomogeneity by the scaled boundary finite element method

In this paper, an enhanced octree polyhedral scaled boundary finite element method (SBFEM) is proposed in which arbitrary convex polygon (pentagon, hexagon, heptagon, octagon etc.) can be directly served as boundary face elements. The presented method overcomes the existing SBFEM's limitation that boundary face is strictly restricted to be a quadrangle or triangle. The conforming shape functions are constructed using a polygon mean-value interpolation scheme for polyhedral face. A highly efficient octree mesh generation technology is introduced to accelerate the progress of pre-treatment, wherein the mesh information can be directly used in the enhanced SBFEM. The accuracy of the proposed method is first verified using a beam under shear and torsion load. Another three more complicated geometries including a nuclear power plant structure, as well as two sculptures named Terra-Cotta Warriors and Sioux Falls Church are presented to demonstrate the application and robustness of the proposed method. The new method possesses appealing versatility and offers a swift adaptive capacity in mesh generation, which can provide a powerful technique for the simulation of complex geometries, rapid-design analysis and multi-scale problems.

An enhanced octree polyhedral scaled boundary finite element method and its applications in structure analysis

A modeling technique based on the scaled boundary finite element method is developed for both static and dynamic analyses of cylindrical shells. A new scaling strategy is employed to ensure that the shell boundaries and the cross sections at the element inferfaces are accurately represented through the scaling process. The formulation starts directly from the three-dimensional linear elasticity theory for cylindrical shells. The principle of virtual work involving the inertial force is applied to derive the scaled boundary finite element equation. Only the in-plane dimensions of the structure are discretized with finite elements while the solution through the thickness is expressed analytically as a Pade expansion. A variable transformation procedure facilitates the development of the dynamic stiffness matrix, which leads to the static stiffness matrix and mass matrix naturally. A laminate model with arbitrary number of layers can readily be constructed. Numerical examples demonstrate the accuracy, applicability and efficiency of the two-layer model.

A scaled boundary finite element method for static and dynamic analyses of cylindrical shells

Semi-analytical analysis of static and dynamic responses for laminated magneto-electro-elastic plates

A unified technique based on the scaled boundary finite element method is presented in this paper to analyze the bending, free vibration and forced vibration of thin to moderately thick beams with constant material properties and rectangular cross sections. The structure model is treated as a plane stress problem and the principle of virtual work involving the inertial force is applied to derive the scaled boundary finite element equation. Higher order spectral elements are used to discretize the longitudinal dimension and the solution through the thickness is expressed analytically as a Pade expansion. A variable transformation technique facilitates the development of the dynamic stiffness matrix, which leads to the static stiffness and mass matrices naturally. Rayleigh damping and Newmark-β method are employed to perform the forced vibration analysis. Numerical examples covering static and dynamic analyses validate the excellent performance and capability of this approach.

Jianghuai Li

Papers

A scaled boundary finite element method for static and dynamic analyses of cylindrical shells

A two-dimensional consistent approach for static and dynamic analyses of uniform beams

An efficient scaled boundary finite element method for transient vibro-acoustic analysis of plates and shells

A unified scaled boundary finite element method for transient two-dimensional vibro-acoustic analysis of plate-like structures