A review of automatic time-stepping strategies on numerical time integration for structural dynamics analysis

2014 ◽  
Vol 80 ◽  
pp. 118-136 ◽  
Author(s):  
Diogo Folador Rossi ◽  
Walnório Graça Ferreira ◽  
Webe João Mansur ◽  
Adenilcia Fernanda Grobério Calenzani
Keyword(s):  
Structural Dynamics ◽  
Time Integration ◽  
Dynamics Analysis ◽  
Time Stepping ◽  
Numerical Time Integration

An Improved Semi-Implicit Method for Structural Dynamics Analysis

1982 ◽  
Vol 49 (3) ◽  
pp. 589-593 ◽  
Author(s):  
K. C. Park
Keyword(s):  
Structural Dynamics ◽  
Truncation Error ◽  
Time Integration ◽  
Implicit Method ◽  
Dynamics Analysis ◽  
Accuracy Improvement ◽  
Implicit Algorithm ◽  
Solution Matrix ◽  
Difference Solution

A semi-implicit algorithm is presented for direct time integration of the structural dynamics equations. The algorithm avoids the factoring of the implicit difference solution matrix and mitigates the unacceptable accuracy losses which plagued previous semi-implicit algorithms. This substantial accuracy improvement is achieved by augmenting the solution matrix with two simple diagonal matrices of the order of the integration truncation error.

IMPROVING STABILITY IN THE TIME-STEPPING ANALYSIS OF STRUCTURAL NONLINEAR DYNAMICS

2008 ◽  
Vol 08 (02) ◽  
pp. 257-270 ◽  
Author(s):  
S. LOPEZ ◽  
K. RUSSO
Keyword(s):  
Structural Dynamics ◽  
Time Integration ◽  
Integration Step ◽  
Two Dimensional ◽  
Motion Equations ◽  
Time Stepping ◽  
Nonlinear Structural Dynamics ◽  
Nonlinear Form ◽  
Newton Iterations ◽  
Discrete Motion

A change in the representation of discrete motion equations for nonlinear structural dynamics of two-dimensional bodies is developed. The objective is to write the motion equation in a less nonlinear form. This leads to a significant increase in the range of stability of the time integration process and a reduction in the number of Newton iterations required in the time integration step.

scholarly journals Modeling Structural Dynamics Using FE-Meshfree QUAD4 Element with Radial-Polynomial Basis Functions

Materials ◽  
2021 ◽  
Vol 14 (9) ◽  
pp. 2288
Author(s):  
Hongming Luo ◽  
Guanhua Sun
Keyword(s):  
Structural Dynamics ◽  
Interpolation Method ◽  
Mass Matrix ◽  
Time Integration ◽  
Partition Of Unity ◽  
Implicit Time ◽  
Lumped Mass ◽  
Point Interpolation Method ◽  
Point Interpolation ◽  
Consistent Mass Matrix

The PU (partition-of-unity) based FE-RPIM QUAD4 (4-node quadrilateral) element was proposed for statics problems. In this element, hybrid shape functions are constructed through multiplying QUAD4 shape function with radial point interpolation method (RPIM). In the present work, the FE-RPIM QUAD4 element is further applied for structural dynamics. Numerical examples regarding to free and forced vibration analyses are presented. The numerical results show that: (1) If CMM (consistent mass matrix) is employed, the FE-RPIM QUAD4 element has better performance than QUAD4 element under both regular and distorted meshes; (2) The DLMM (diagonally lumped mass matrix) can supersede the CMM in the context of the FE-RPIM QUAD4 element even for the scheme of implicit time integration.

DQFEM Analyses of Static and Dynamic Nonlinear Elastic-Plastic Problems Using a GSR-Based Accelerated Constant Stiffness Equilibrium Iteration Technique

2001 ◽  
Vol 123 (3) ◽  
pp. 310-317 ◽  
Author(s):  
Chang-New Chen
Keyword(s):  
Finite Element ◽  
Numerical Technique ◽  
Time Integration ◽  
Differential Quadrature ◽  
Element Discretization ◽  
Constant Stiffness ◽  
Structural Problems ◽  
Nonlinear Structural ◽  
Numerical Time Integration ◽  
Nonlinear Elastic

An integrated numerical technique for static and dynamic nonlinear structural problems adopting the equilibrium iteration is proposed. The differential quadrature finite element method (DQFEM), which uses the differential quadrature (DQ) techniques to the finite element discretization, is used to analyze the static and dynamic nonlinear structural mechanics problems. Numerical time integration in conjunction with the use of equilibrium iteration is used to update the response history. The equilibrium iteration can be carried out by the accelerated iteration schemes. The global secant relaxation-based accelerated constant stiffness and diagonal stiffness-based predictor-corrector equilibrium iterations which are efficient and reliable are used for the numerical computations. Sample problems are analyzed. Numerical results demonstrate the algorithm.

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