Dynamic Response
J. Akbari; S. Mirzaei
Abstract
Numerical techniques for solving dynamic structural problems often encounter significant challenges, including conditional stability, period elongation errors, amplitude decay errors, and the emergence of spurious frequencies. To address these issues, several first-order precise integration methods have ...
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Numerical techniques for solving dynamic structural problems often encounter significant challenges, including conditional stability, period elongation errors, amplitude decay errors, and the emergence of spurious frequencies. To address these issues, several first-order precise integration methods have been developed; however, these approaches still suffer from errors associated with the inversion of the state matrix. This study employs the singular value decomposition technique to enhance the efficiency of the precise integration method algorithm and eliminate the singularity of the state matrix. The robustness of the proposed method is evaluated across various transient dynamic problems. The results demonstrate that traditional approaches, such as the Newmark method, exhibit substantially larger errors—exceeding 150% in certain cases. Ultimately, the findings emphasize that accurately estimating the dynamic response of multi-degree-of-freedom systems under impact loading requires careful consideration. Conventional methods, including the Newmark average acceleration technique, should therefore not be applied indiscriminately.
Dynamic Response
J. Akbari; H. Valaei; M. F. Sepahvand
Abstract
Finite-element modeling of structures using elements without rotational degrees of freedom (DOFs) is usually stiffer than their physical behavior. Therefore, the stiffness of a structural system will be smoothed by adding rotational DOFs in the numerical model. In the traditional displacement-based ...
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Finite-element modeling of structures using elements without rotational degrees of freedom (DOFs) is usually stiffer than their physical behavior. Therefore, the stiffness of a structural system will be smoothed by adding rotational DOFs in the numerical model. In the traditional displacement-based finite-element method, adding drilling rotations is not easy. The main contribution of this paper is performing dynamic analyses using the finite strip element with added drilling rotations to the elements. For this purpose, any quadrilateral area is divided into two independent sets of orthogonal strips comprising truss and Bernoulli-Euler beam elements. Then, by using new shape functions, mass, damping, stiffness matrices, and equivalent nodal forces are derived. Finally, time history analysis for plane stress or strain type problems for direct earthquake records is performed using the developed formulations. The numerical studies show that the results of the finite strip element method using coarse meshes are competitive with the results of the finite-element method using fine meshes. This advantage is valuable in time-consuming computational problems, e.g., dynamic or nonlinear analyses.
