Nonlinear Dynamic Analysis of a Structure Subjected to Multiple Support Motions

1981 ◽  
Vol 103 (1) ◽  
pp. 27-32 ◽  
Author(s):  
V. N. Shah ◽  
A. J. Hartmann
Keyword(s):  
Rigid Body ◽  
Dynamic Analysis ◽  
Nonlinear Dynamic ◽  
Nonlinear Dynamic Analysis ◽  
Rigid Body Motion ◽  
Body Motion ◽  
Superposition Method ◽  
Modal Superposition ◽  
Modal Superposition Method ◽  
Multiple Support

A modal superposition method for the nonlinear dynamic analysis of a structure subjected to multiple support motions is presented. The nonlinearities are due to clearances between the components and their supports. The finite element method is used to derive the equations of motion with the nonlinearities represented by a pseudo force vector. The displacement response may be divided into two parts: elastic deformation and rigid body motion. The presence of rigid body motion necessitates the inclusion of the higher modes in the transient analysis. The modal superposition method is used to analyze the dynamic response of one loop of the nuclear steam supply system. This loop has nonlinear supports and is subjected to nonuniform seismic excitations at the supports. It is shown that the computational cost of the modal superposition method is lower than that of the direct integration.

Seismic Analysis of Structures With Coulomb Friction

1983 ◽  
Vol 105 (2) ◽  
pp. 171-178 ◽  
Author(s):  
V. N. Shah ◽  
C. B. Gilmore
Keyword(s):  
Rigid Body ◽  
Coulomb Friction ◽  
Seismic Event ◽  
Seismic Analysis ◽  
Equations Of Motion ◽  
Relative Displacement ◽  
Rigid Body Motion ◽  
Body Motion ◽  
Superposition Method ◽  
Modal Superposition Method

A modal superposition method for the dynamic analysis of a structure with Coulomb friction is presented. The finite element method is used to derive the equations of motion, and the nonlinearities due to friction are represented by pseudo-force vector. A structure standing freely on the ground may slide during a seismic event. The relative displacement response may be divided into two parts: elastic deformation and rigid body motion. The presence of rigid body motion necessitates the inclusion of the higher modes in the transient analysis. Three single degree-of-freedom problems are solved to verify this method. In a fourth problem, the dynamic response of a platform standing freely on the ground is analyzed during a seismic event.

Automated Analysis of Constrained Systems of Rigid and Flexible Bodies

1985 ◽  
Vol 107 (4) ◽  
pp. 431-439 ◽  
Author(s):  
A. A. Shabana
Keyword(s):  
Rigid Body ◽  
Dynamic Analysis ◽  
Mass Matrix ◽  
Ritz Method ◽  
Rigid Body Motion ◽  
Constrained Systems ◽  
Body Motion ◽  
Lumped Mass ◽  
Flexible Bodies ◽  
Inertia Properties

This paper is concerned with modeling inertia properties of flexible components that undergo large angular rotations. Consistent, lumped and hybrid mass techniques are presented in detail and used to model the inertia properties of flexible bodies. The consistent formulation allows using the finite-element method as well as Rayleigh-Ritz method to describe the deformation of elastic components. Lumped mass techniques allow using shape vectors or experimentally identified data. In the hybrid mass formulation, the flexibility mass matrix is evaluated using a consistent mass formulation, while the inertia coupling between gross rigid body motion and elastic deformation is formulated using a lumped mass technique. Different mass formulations require the evaluation of similar sets of time-invariant matrices that represent the inertia coupling. Consequently, these matrices have to be evaluated only once in advance for the dynamic analysis. A unified mathematical model, and accordingly a unified computer program (DAMS: Dynamic Analysis of Multibody Systems), that deal with different formulations are developed. A comparative study is presented in order to study the effect of the mass formulation on the dynamic response of elastodynamic constrained systems. The validity of the linear theory that neglects the effect of small oscillations on large rigid body motion is also discussed.

An Efficient and Robust Nonlinear Dynamic Analysis Method for Framed Structures Using the Rigid Body Rule

2021 ◽  
Author(s):  
Zhaohui Chen ◽  
Min He ◽  
Yuchen Tao ◽  
Y. B. Yang
Keyword(s):  
Rigid Body ◽  
Dynamic Analysis ◽  
Nonlinear Dynamic ◽  
Integration Method ◽  
Nonlinear Dynamic Analysis ◽  
Direct Integration ◽  
Analysis Method ◽  
Framed Structures ◽  
Geometric Stiffness ◽  
Highly Nonlinear

In this paper, by implanting the rigid body rule (RBR)-based strategy for static nonlinear problems into the implicit direct integration procedure, an efficient and robustness nonlinear dynamic analysis method for the response of framed structures with large deflections and rotations is proposed. The implicit integration method proposed by Newmark is improved by inserting an intermediate time into the time step and by adding the 3-point backward difference in the second substep so as to preserve the momentum conservation and to maintain the stability of the direct integration method. To solve the equivalent incremental equations of motion, the RBR is built in to deal with the rigid rotations and the resulting additional nodal forces of element. During the increment-iterative procedure, the use of RBR-qualified geometric stiffness in the predictor reduces the numbers of iterations, while the elastic stiffness alone in the corrector to update the element nodal forces makes the computation efficiency and convergence with no virtual forces caused by the ill geometric stiffness. The proposed algorithm is advanced in the applications of several framed structures with highly nonlinear behavior in the dynamic response by its simplicity, efficient and robustness.

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