Article

A new algorithm for numerical solution of dynamic elastic–plastic hardening and softening problems

Department of Civil and Environment Engineering, University of California, Los Angeles, Los Angeles, CA 90095-1593, USA
Computers & Structures (Impact Factor: 2.18). 08/2003; DOI: 10.1016/S0045-7949(03)00167-6

ABSTRACT The objective of this paper is to develop a new algorithm for numerical solution of dynamic elastic–plastic strain hardening/softening problems, particularly for the implementation of the gradient dependent model used in solving strain softening problems. The new algorithm for the solution of dynamic elastic–plastic problems is derived based on the parametric variational principle. The gradient dependent model is employed in the numerical model to overcome the mesh-sensitivity difficulty in dynamic strain softening or strain localization analysis. The precise integration method, which has been used for the solution of linear problems, is adopted and improved for the solution of dynamic non-linear equations. The new algorithm is proposed by taking the advantages of the parametric quadratic programming method and the precise integration method. Results of numerical examples demonstrate the validity and the advantages of the proposed algorithm.

Full-text

Available from: Jiun-Shyan Chen, Apr 17, 2015
0 Followers
 · 
174 Views
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: Structures composed of physical nonlinear finite elements under bending and compression or tension are considered in this paper. Material nonlinearity is considered as linearly hardened. In case of material hardening, plastic strains do not concentrate in one point but distribute in the certain volumes of finite element. Volumes of plas-tic strains zones in frame structure elements impact on elasticity modules of these elements sections by decreasing them. Technique of such elasticity modules decrease in finite elements sections is suggested. To realize such structure analysis, a treatment of strains in mathematical model is changed. Now strains are treated not as rotation angles and elongations of finite elements, but as longitudinal strains. Mathematical model including above mentioned modifica-tions is presented. Solving algorithm based on a modified Newton-Raphson method is particularly explained and employed for numerical example.
  • [Show abstract] [Hide abstract]
    ABSTRACT: A fast precise integration method (FPIM) is proposed for solving structural dynamics problems. It is based on the original precise integration method (PIM) that utilizes the sparse nature of the system matrices and especially the physical features found in structural dynamics problems. A physical interpretation of the matrix exponential is given, which leads to an efficient algorithm for both its evaluation and subsequently the solution of large-scale structural dynamics problems. The proposed algorithm is accurate, efficient and requires less computer storage than previous techniques.
    Structural Engineering & Mechanics 07/2012; 43(1). DOI:10.12989/sem.2012.43.1.001 · 0.80 Impact Factor
  • [Show abstract] [Hide abstract]
    ABSTRACT: Based on the subdomain parametric variational principle (SPVP), a contact analysis approach is formulated in the incremental form for 2D solid mechanics problems discretized using only triangular elements. The present approach is implemented for the newly developed node-based smoothed finite element method (NS-FEM), the edge-based smoothed finite element method (ES-FEM) as well as standard FEM models. In the approach, the contact interface equations are discretized by contact point-pairs using a modified Coulomb frictional contact model. For strictly imposing the contact constraints, the global discretized system equations are transformed into a standard linear complementarity problem (LCP), which can be readily solved using the Lemke method. This approach can simulate different contact behaviors including bonding/debonding, contacting/departing, and sticking/slipping. An intensive numerical study is conducted to investigate the effects of various parameters and validate the proposed method. The numerical results have demonstrated the validity and efficiency of the present contact analysis approach as well as the good performance of the ES-FEM method, which provides solutions of about 10 times better accuracy and higher convergence rate than the FEM and NS-FEM methods. The results also indicate that the NS-FEM provides upper-bound solutions in energy norm, relative to the fact that FEM provides lower-bound solutions.
    Engineering Analysis with Boundary Elements 10/2013; 37(10). DOI:10.1016/j.enganabound.2013.06.003 · 1.44 Impact Factor