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

State Key Laboratory of Structural Analysis and Industrial Equipment, Department of Engineering Mechanics, Dalian University of Technology, Dalian 116024, PR China; Department of Civil and Environment Engineering, University of California, Los Angeles, Los Angeles, CA 90095-1593, USA
Computers & Structures (Impact Factor: 2.18). 01/2003; 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.

  • [Show abstract] [Hide abstract]
    ABSTRACT: In this chapter, a second-order scheme of precise time-step integration (PTI) method is introduced for dynamic analysis with respect to long-term integration and transient responses while spatial discretization is realized with the differential quadrature method. Rather than transforming into first-order equations, a recursive scheme is presented in detail for direct solution of the homogeneous part of second-order differential and algebraic equations. The sine and cosine matrices involved in the scheme are calculated using the so-called N 2 algorithm, and the corresponding particular solution is also presented where the excitation vector is approximated by the truncated Taylor series. The performance and numerical behaviors of the second-order scheme of the PTI method are tested by a series of numerical examples in comparison with the first-order scheme or with the traditional time-marching Newmark-β method as the reference. The issue of spurious high-frequency responses resulting from spatial discretization for shock-excited structural dynamic analysis is also studied in the framework of the second-order PTI method. The effects of spatial discretization, numerical damping and time step on solution accuracy are explored by analyzing longitudinal vibrations of a shock-excited rod with rectangular, half-triangular and Heaviside step impact.
  • [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). · 0.80 Impact Factor
  • [Show abstract] [Hide abstract]
    ABSTRACT: This paper presents a simulation study of the free flexural vibration behavior of non-uniform taper bars of circular and rectangular cross-section under body force loading due to gravity. The loading is controlled statically to take the bar to its post-elastic state so as to predict its dynamic behavior in the presence of plastic deformation. Hence the analysis is carried out in two parts; first the static problem under axial gravity loading is solved, then the dynamic problem is solved in this loaded condition. Appropriate variational method is employed to derive the set of governing equations for both the problems. The formulation is based on unknown displacement field which is approximated by finite linear combinations of orthogonal admissible functions. The present method is validated successfully with a well-known finite element package. Results are presented to investigate the effect of shape and size on the dynamic behavior of non-uniform taper bars. The study can be extended to study the post-elastic dynamic behavior of other related problems such as rotating beams and rotating disks.
    Applied Mathematical Modelling 01/2009; 33(11):4163-4183. · 2.16 Impact Factor

Full-text (2 Sources)

Available from
May 21, 2014