Chih-Wen Chang^*

CMC-Computers, Materials & Continua, Vol.73, No.1, pp. 433-451, 2022, DOI:10.32604/cmc.2022.027021

Abstract We retrieve unknown nonlinear large space-time dependent forces burdened with the vibrating nonlinear Euler-Bernoulli beams under varied boundary data, comprising two-end fixed, cantilevered, clamped-hinged, and simply supported conditions in this study. Even though some researchers used several schemes to overcome these forward problems of Euler-Bernoulli beams; however, an effective numerical algorithm to solve these inverse problems is still not available. We cope with the homogeneous boundary conditions, initial data, and final time datum for each type of nonlinear beam by employing a variety of boundary shape functions. The unknown nonlinear large external force can be recuperated via back-substitution of the… More >

Chein-Shan Liu¹, Chung-Lun Kuo²

CMES-Computer Modeling in Engineering & Sciences, Vol.76, No.2, pp. 109-132, 2011, DOI:10.3970/cmes.2011.076.109

Abstract The Tikhonov method is a famous technique for regularizing ill-posed systems. In this theory a regularization parameter α needs to be determined. Based-on an invariant-manifold defined in the space of (x,t) and from the Tikhonov minimization functional, we can derive an optimal vector driven system of nonlinear ordinary differential equations (ODEs). In the Optimal Vector Driven Algorithm (OVDA), the optimal regularization parameter αk is presented in the iterative solution of x, which means that a dynamical Tikhonov regularization method is involved in the solution of nonlinear ill-posed problem. The OVDA is an extension of the Landweber-Scherzer iterative algorithm. Numerical examples… More >

Linjun Wang¹, Xu Han², Youxiang Xie³

CMES-Computer Modeling in Engineering & Sciences, Vol.82, No.3&4, pp. 179-194, 2011, DOI:10.32604/cmes.2011.082.179

Abstract In this paper, a new homotopy perturbation method (IHPM) is presented and suggested to solve an ill-posed problem of multi-source dynamic loads reconstruction. We propose a stable and reliable modification, and obtain a new regularization method, then employ it to find the exact solution for the multi-source dynamic load identification problem. Also, this present method only needs easy computations rather than successive integrations. Finally, the performances of two numerical examples are given. Comparisons are performed between the original homotopy perturbation method (HPM) and IHPM. The results verify that the present method is very simple and effective. More >