scholarly journals A Robust and Efficient Composite Time Integration Algorithm for Nonlinear Structural Dynamic Analysis

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
Lihong Zhang ◽  
Tianyun Liu ◽  
Qingbin Li
Keyword(s):  
Finite Element ◽  
Time Integration ◽  
Computational Cost ◽  
Nonlinear Problems ◽  
Central Difference ◽  
Integration Algorithm ◽  
Structural Dynamic ◽  
Nonlinear Structural ◽  
Time Integration Algorithm ◽  
Difference Formula

This paper presents a new robust and efficient time integration algorithm suitable for various complex nonlinear structural dynamic finite element problems. Based on the idea of composition, the three-point backward difference formula and a generalized central difference formula are combined to constitute the implicit algorithm. Theoretical analysis indicates that the composite algorithm is a single-solver algorithm with satisfactory accuracy, unconditional stability, and second-order convergence rate. Moreover, without any additional parameters, the composite algorithm maintains a symmetric effective stiffness matrix and the computational cost is the same as that of the trapezoidal rule. And more merits of the proposed algorithm are revealed through several representative finite element examples by comparing with analytical solutions or solutions provided by other numerical techniques. Results show that not only the linear stiff problem but also the nonlinear problems involving nonlinearities of geometry, contact, and material can be solved efficiently and successfully by this composite algorithm. Thus the prospect of its implementation in existing finite element codes can be foreseen.

An Improved Time Integration Algorithm: A Collocation Time Finite Element Approach

2017 ◽  
Vol 17 (02) ◽  
pp. 1750024 ◽  
Author(s):  
Wooram Kim ◽  
J. N. Reddy
Keyword(s):  
Finite Element ◽  
Time Integration ◽  
Integration Algorithm ◽  
Finite Element Approach ◽  
New Family ◽  
Integration Schemes ◽  
Time Integration Algorithm ◽  
Time Integration Schemes ◽  
Element Approach ◽  
Integration Algorithms

A time collocation finite element approach is employed to develop one- and two-step time integration schemes with algorithmic dissipation control capability. The newly developed time integration schemes are combined to obtain a new family of time integration algorithms using the concept employed by Baig and Bathe. The newly developed algorithm can effectively control the algorithmic dissipation by relating the collocation parameters with the spectral radius in the high frequency limit. The new algorithm provides better accuracy compared with the generalized-[Formula: see text] method for highly dissipative cases and includes the Baig and Bathe method within its family as a special case.

Time Integration Method Based on Discrete Transfer Function

2016 ◽  
Vol 16 (05) ◽  
pp. 1550009 ◽  
Author(s):  
M. Rezaiee-Pajand ◽  
M. Hashemian
Keyword(s):  
Transfer Function ◽  
Time Integration ◽  
Integration Algorithm ◽  
Structural Dynamic ◽  
Time Integration Algorithm ◽  
Integration Techniques ◽  
Complex Structural ◽  
Nonlinear Dynamic Analyses ◽  
Explicit Time Integration Algorithm ◽  
Discrete Transfer Function

Complex structural dynamic problems are normally analyzed by finite element and numerical integration techniques. An explicit time integration algorithm with second-order accuracy and unconditional stability is presented for dynamic analysis. Utilizing weighted factors, the current displacement and velocity relations are defined in terms of the accelerations of two previous time steps. The concept of discrete transfer function and the pole mapping rule from the control theory are exploited to develop the new algorithm. Several linear and nonlinear dynamic analyses are performed to verify the efficiency of the method compared with the well-known Newmark method.

An explicit time integration algorithm for linear and non-linear finite element analyses of dynamic and wave problems

2018 ◽  
Vol 36 (1) ◽  
pp. 161-177 ◽  
Author(s):  
Mi Zhao ◽  
Huifang Li ◽  
Shengtao Cao ◽  
Xiuli Du
Keyword(s):  
Finite Element ◽  
Time Integration ◽  
Single Step ◽  
Degree Of Freedom ◽  
Integration Algorithm ◽  
Explicit Time Integration ◽  
Content Type ◽  
Time Integration Algorithm ◽  
Non Linear ◽  
Explicit Time Integration Algorithm

Purpose The purpose of this paper is to propose a new explicit time integration algorithm for solution to the linear and non-linear finite element equations of structural dynamic and wave propagation problems. Design/methodology/approach The algorithm is completely explicit so that no linear equation system requires solving, if the mass matrix of the finite element equation is diagonal and whether the damping matrix does or not. The algorithm is a single-step method that has the simple starting and is applicable to the analysis with the variable time step size. The algorithm is second-order accurate and conditionally stable. Its numerical stability, dissipation and dispersion are analyzed for the dynamic single-degree-of-freedom equation. The stability of the multi-degrees-of-freedom non-proportional damping system can be evaluated directly by the stability theory on ordinary differential equation. Findings The performance of the proposed algorithm is demonstrated by several numerical examples including the linear single-degree-of-freedom problem, non-linear two-degree-of-freedom problem, wave propagation problem in two-dimensional layer and seismic elastoplastic analysis of high-rise structure. Originality/value A new single-step second-order accurate explicit time integration algorithm is proposed to solve the linear and non-linear dynamic finite element equations. The algorithm has advantages on the numerical stability and accuracy over the existing modified central difference method and Chung-Lee method though the theory and numerical analyses.

scholarly journals Explicit Dynamic Finite Element Method for Failure with Smooth Fracture Energy Dissipations

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Jeong-Hoon Song ◽  
Thomas Menouillard ◽  
Alireza Tabarraei
Keyword(s):  
Finite Element ◽  
Fracture Energy ◽  
Computational Cost ◽  
Quadrature Rule ◽  
Dynamic Failure ◽  
Structural Dynamic ◽  
Integration Schemes ◽  
Hourglass Control ◽  
Quadrilateral Finite Element ◽  
Explicit Dynamic

A numerical method for dynamic failure analysis through the phantom node method is further developed. A distinct feature of this method is the use of the phantom nodes with a newly developed correction force scheme. Through this improved approach, fracture energy can be smoothly dissipated during dynamic failure processes without emanating noisy artifact stress waves. This method is implemented to the standard 4-node quadrilateral finite element; a single quadrature rule is employed with an hourglass control scheme in order to decrease computational cost and circumvent difficulties associated with the subdomain integration schemes for cracked elements. The effectiveness and robustness of this method are demonstrated with several numerical examples. In these examples, we showed the effectiveness of the described correction force scheme along with the applicability of this method to an interesting class of structural dynamic failure problems.

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.

Impact Dynamic Analysis of Horizontally Vibrated Conveyor with Coulomb Friction Modeling

2012 ◽  
Vol 619 ◽  
pp. 26-29
Author(s):  
Chao Sheng Song ◽  
Qi Ming Huang ◽  
Zhan Gao ◽  
Jie Xu
Keyword(s):  
Coulomb Friction ◽  
Impact Analysis ◽  
Time Integration ◽  
Impact Excitation ◽  
Friction Modeling ◽  
Integration Algorithm ◽  
Conveyor System ◽  
Time Integration Algorithm ◽  
And Control ◽  
The Impact

This paper introduces dynamic impact analysis as an effective technique for studying the response of horizontal vibrated conveyor with time-varying impact excitation by the falling of the scrap. A two degree-of-freedoms impact dynamic model is formulated considering the static and dynamic coulomb friction between the scrap and chute. Then the time integration algorithm was applied in the program to solve the dynamic equations. Using the proposed method, the impact effects of ideal single scrap and multiple scraps on the dynamic response of the conveyor were analyzed. Computational results reveal numerous interesting dynamic characteristics which can be used to forecast and control the vibration of the scrap and conveyor system.

Sign in / Sign up

Export Citation Format

Share Document