SUMMARY A novel method called immersed smoothed FEM using three‐node triangular element is proposed for two‐dimensional fluid–structure interaction (FSI) problems with largely deformable nonlinear solids placed within incompressible viscous fluid. The fluid flows are solved using the semi‐implicit characteristic‐based split method. Smoothed FEMs are employed to calculate the transient responses of solids based on explicit time integration. The fictitious fluid with two assumptions is introduced to achieve the continuous form of the FSI conditions. The discrete formulations to calculate the FSI forces are obtained in terms of the characteristic‐based split scheme, and the algorithm based on a set of fictitious fluid mesh is proposed for evaluating the FSI force exerted on the solid. The accuracy, stability, and convergence properties of immersed smoothed FEM are verified by numerical examples. Investigations on the mesh size ratio indicate that the stability is fairly independent of the wide range of the mesh size ratio. No additional volume correction is required to satisfy the incompressible constraints. Copyright © 2012 John Wiley & Sons, Ltd.

This paper proposes a rapid inverse analysis approach based on the reduced basis method and the Levenberg-Marquardt-Fletcher algorithm to identify the "unknown" material properties: Young's modulus and stiffness-proportional Rayleigh damping coefficient of the interfacial tissue between a dental implant and the surrounding bones. In the forward problem, a finite element approximation for a three-dimensional dental implant-bone model is first built. A reduced basis approximation is then established by using a Proper Orthogonal Decomposition (POD)-Greedy algorithm and the Galerkin projection to enable extremely fast and reliable computation of displacement responses for a range of material properties. In the inverse analysis, the reduced basis approximation for the dental implant-bone model are incorporated in the Levenberg-Marquardt-Fletcher algorithm to enable rapid identification of the unknown material properties. Numerical results are presented to demonstrate the efficiency and robustness of the proposed method.

A three-dimensional Immersed Smoothed Finite Element Method (3D IS-FEM) using 4-node tetrahedral element is proposed to solve 3D fluid-structure interaction (FSI) problems. The 3D IS-FEM is able to determine accurately the physical deformation of the nonlinear solids placed within the incompressible viscous fluid governed by Navier-Stokes equations. The method employs the semi-implicit Characteristic-Based Split (CBS) scheme to solve the fluid flows and Smoothed Finite Element Methods (S-FEM) to calculate the transient dynamics responses of the nonlinear solids based on explicit time integration. To impose the FSI conditions, a novel, effective and sufficiently general technique via simple linear interpolation is presented based on Lagrangian fictitious fluid meshes coinciding with the moving and deforming solid meshes. In the comparisons to the referenced works including experiments, it is clear that the proposed 3D IS-FEM ensures stability of the scheme with the second order spatial convergence property; and the IS-FEM is fairly independent of a wide range of mesh size ratio.

To improve the safety performance and maintain light weight of composite automotive bumper beams subjected to low-velocity impacts, a structural optimization and a novel reliability analysis procedure for multi-objectives are established in this paper. Both longitudinal and corner pendulum impacts are considered, and the optimized bumper beam has significant improvements. Compared with the original composite bumper beam, the section force of the crash box in the corner pendulum impact and the mass of the optimal bumper beam are decreased by 9.6% and 20.3%, respectively. The novel reliability analysis results show that the knee point may be less reliable whereas the design with inferior knee point is of higher reliability. Therefore, a design on an inferior knee point may be more attractive in engineering design practices. Our numerical results have demonstrated that the optimization procedure established in this paper to improve the performance of composite bumper beams and our proposed reliability analysis method considering multi-objectives are effective and useful in the engineering design of bumper beams. These techniques are also useful for the design of other types of structural components where weight and safety are of importance.