Search

Abstract: Approximate techniques have been developed to calculate eigenvalues of structural system in a reduced manner. However, the construction of a reduced system is problematic with regard to localized selection of the important degrees of freedom and excessive computing time. Recently, a scheme that combines a subdomain method and a reduced system has been proposed as a means of overcoming these problems. Although the combined method is more efficient than previous reduction methods, we still suffer from one aspect: namely, it tends to produce a number of subdomains without any boundary constraints when partitioning the global domain. The Ritz vector estimation is required to be extracted in the selection process of the primary degrees of freedom. The Ritz vector of each subdomain can be easily obtained through a general static analysis of a subdomain with a boundary constraint. In contrast, a pseudo-inverse calculation takes considerable computing time to obtain the reduced system of a floating subdomain without any boundary constraints. This problem can be overcome by using the reduced pseudo-inverse method based on static condensation, which is not related to the selection of the primary degrees of freedom for eigenvalue analysis of given structure. Numerical examples demonstrate that the proposed scheme effectively reduces the computational cost in the process of primary degree-of-freedom selection. In addition, the reduced system based on the proposed scheme can accurately predict the eigenvalues of a global system as well as the time response under dynamic loads. [Copyright &y& Elsevier]

Abstract: A large number of eigenmodes are required for the realistic simulation of the object under arbitrary dynamic load such as impact load while only a few lower modes are adequate for the simulation of free vibration with initial deformation. For the accurate dynamic simulation under impact, a large amount of computer resources are required to obtain considerable number of eigenpairs. The present study presents an efficient dynamic simulation algorithm and simulation results of elastically deformable body under impact. We employ a modal analysis technique that pre-computes the eigenvalues and the corresponding eigenvectors in the framework of finite element method. For low latency time of real-time simulation, eigenmodes are computed from a reduced system constructed from the original one. To construct reduced system, energy estimation technique in the element level is proposed in the present study. Through a number of examples, it is demonstrated that the proposed method saves computational cost effectively and provides reliable real time results of the deformable solids under impact. [Copyright &y& Elsevier]

Abstract: In the design sensitivity analysis, the adjoint variable method has been widely used for the sensitivity calculation. The adjoint variable method can reduce computation time and save computer resources because it can provide the sensitivity values only at the positions in which designers are willing to obtain. However, exact analytical differentiation with respect to the design variables is commonly employed in adjoint variable method. Although the exact derivative assures the accurate sensitivity, it is cumbersome to take differentiation in an exact manner for every given type of finite element. Therefore, in the present study, a new improved semi-analytic design sensitivity method is proposed in the framework of adjoint variable method. Recently, a numerical inaccuracy trouble in the traditional semi-analytic method has been settled by the rigid body mode separation technique and high order approximation scheme. Combining the adjoint variable method with improved semi-analytic design sensitivity scheme, the design sensitivity value can be calculated accurately and efficiently. Through numerical examples, the efficiency and accuracy of the proposed semi-analytic sensitivity scheme in the adjoint variable method are demonstrated. [Copyright &y& Elsevier]