Element Reanalysis Research Articles

Quality optimization of liquid silicon lenses based on sequential approximation optimization and radial basis function networks

This study introduces an innovative multi-objective optimization method based on sequential approximation optimization (SAO) and radial basis function (RBF) networks to enhance the injection molding process for liquid silicone optical lenses. The method successfully minimizes residual stress and volume shrinkage, thereby improving product quality and manufacturing efficiency. By replacing finite element reanalysis with the RBF network, it constructs an approximate functional relationship between process conditions and quality. The novelty lies in simplifying multi-objective optimization into a single-objective problem and utilizing Pareto boundary analysis for precise parameter tuning. This approach not only reduces trial-and-error costs and material waste but also significantly decreases carbon emissions, showcasing extensive potential for application in various manufacturing processes. Simulations varying key parameters—filling time, melt temperature, mold temperature, curing pressure, and curing time—revealed optimal conditions: filling time of 1.57s, melt temperature of 27.18 °C, mold temperature of 150 °C, curing time of 20.02s, and curing pressure of 28.79 MPa. Experiments were conducted to validate the numerical results, employing nondestructive testing methods to assess residual stress and volume shrinkage. The results demonstrated significant reductions in these values, affirming the method’s reliability and practicality. This innovative and efficient optimization approach provides a robust solution for enhancing injection molding processes while contributing to sustainability and cost efficiency.

A fast reanalysis solver for 3D transient thermo-mechanical problems with temperature-dependent materials

A fast reanalysis solver using linear tetrahedral elements is developed for 3D transient thermo-mechanical problems with temperature-dependent materials. The core idea is to formulate the reanalysis framework of a stable node-based smoothed finite element reanalysis method. In the developed solver, the stable node-based smoothed finite element method (SNS-FEM) is used as the main solver due its accuracy and stability. The combined approximations (CA) method is the auxiliary tool for improving the efficiency of the SNS-FEM. In the developed reanalysis framework, binomial series expressions are used as high-quality basis vectors for the reduced basis method. The transient temperature and displacement fields can then be calculated without solving the complete set of nonlinear or linear system equations. The performance of the developed solver is evaluated through several numerical examples with different kinds of mixed boundary conditions. The results show that the reanalysis framework with two or three basis vectors is 20–50 times faster than the complete analysis and that the solver is much more efficient and stable than other solvers that use the traditional finite element method (FEM) or the smoothed finite element method (NS-FEM). Therefore, the performance of the developed solver is demonstrated.

Study on process parameters and its analytic application for nonaxisymmetric rectangular cup of multistage deep drawing process using low carbon thin steel sheet

Multistage deep drawing process is widely used to obtain various nonaxisymmetric rectangular cups. This deep drawing scheme including drawing and ironing processes consists of several tool sets to carry out a continuous production within one progressive press. To achieve the successive production, design and fabrication of the necessary tools such as punch, die, and other auxiliary devices are critical, therefore, a series of process parameters play an important role in performing the process design. This study focuses on the tool design and modification for developing the rectangular cup with an aspect ratio of 5.7, using cold-rolled low carbon thin steel sheet with the initial thickness of 0.4 mm. Based on the design results for the process and the tools, finite element analysis for the multistage deep drawing process is performed with thickness control of the side wall in intermediate blanks as the first approach. From the results of the first approach, it is shown that the intermediate blanks could experience failures such as tearing, wrinkling, and earing by excessive thinning and thickening. To solve these failures, the modifications for the deep drawing punches are carried out, and the modified punches are applied to the same process. The simulation results for the multistage rectangular deep drawing process are compared with the thickness distributions before and after the punch shape modifications, and with the deformed shape in each intermediate blank, respectively. The results of finite element reanalysis using the modified punches show significant improvement compared with those by using the original designed punch shapes.

Design Optimization for Structural-Acoustic Problems Using FEA-BEA With Adjoint Variable Method

A noise-vibration-harshness (NVH) design optimization of a complex vehicle structure is presented using finite element and boundary element analyses. The steady-state dynamic behavior of the vehicle is calculated from the frequency response finite element analysis, while the sound pressure level within the acoustic cavity is calculated from the boundary element analysis. A reverse solution process is employed for the design sensitivity calculation using the adjoint variable method. The adjoint load is obtained from the acoustic boundary element re-analysis, while the adjoint solution is calculated from the structural dynamic re-analysis. The evaluation of pressure sensitivity only involves a numerical integration process over the structural part where the design variable is defined. A design optimization problem is formulated and solved, where the structural weight is reduced while the noise level in the passenger compartment is lowered.

Design sensitivity analysis for sequential structural–acoustic problems

A design sensitivity analysis of a sequential structural–acoustic problem is presented in which structural and acoustic behaviors are de-coupled. A frequency-response analysis is used to obtain the dynamic behavior of an automotive structure, while the boundary element method is used to solve the pressure response of an interior, acoustic domain. For the purposes of design sensitivity analysis, a direct differentiation method and an adjoint variable method are presented. In the adjoint variable method, an adjoint load is obtained from the acoustic boundary element re-analysis, while the adjoint solution is calculated from the structural dynamic re-analysis. The evaluation of pressure sensitivity only involves a numerical integration process for the structural part. The proposed sensitivity results are compared to finite difference sensitivity results with excellent agreement.

A reduction method for boundary element reanalysis

This paper is concerned with reanalysis for boundary element systems. An efficient and accurate reduction method is proposed for reanalyzing such systems. The new method has several merits. In particular, the reduced system has been uncoupled by a Gram–Schmidt orthonormalization procedure. Also, a computation-inexpensive convergence criterion is proposed for the automatic determination of the number of basis vectors required to approximate the solution within a specified level of accuracy. Several example problems are illustrated to verify the accuracy and efficiency of the proposed reduction method.

Iteration schemes for improved convergence in boundary element reanalysis

For large changes in design, the simple iteration scheme for reanalysis with the boundary element method shows a poor convergence. A variety of techniques to improve the convergence of these iterations are presented. The effect of modified Aitken's acceleration process on the simple iterations for reanalysis is determined. These developments are applied for the reanalysis of both the structural response and design sensitivities. The number of arithmetic operations required for each of the iteration schemes considered are given to compare the relative efficiencies of these schemes. While all the schemes for improving convergence of the reanalysis procedure demonstrate advantageous results, no single method is seen to be clearly superior to the rest for boundary element reanalysis. The advantages of the proposed procedure are demonstrated by numerical examples.

Finite element reanalysis of real eigenvalue problem. Case study of vibration eigenvalue.

An attempt is made to formulate the finite element reanalysis to cope with the change of vibration eigenvalues and eigenvectors. The methodology is based upon iterative solution of the nonlinear, coupled equations with respect to the change of the eigen pairs. Use is made of the normalization condition of the eigenvectors. Two methods are proposed for the solution, and the first one requires less CPU time while the second is versatile enough to chase complicated change of the eigen pair. The numerical examples show the validity of the proposed reanalysis methods in regard to the vibration of portal frames which are subjected to so large structural modification in terms of the mass density and the modulus of elasticity that the eigenvector is changed markedly.