Efficient implementation of an explicit partitioned shear and longitudinal wave propagation algorithm

Abstract

SUMMARYThe paper complements and extends the previous works on partitioned explicit wave propagation analysis methods, which were presented for discontinuous wave propagation problems in solids. An efficient implementation of the partitioned explicit wave propagation analysis methods is introduced. The present implementation achieves about 25% overall computational effort compared with the previous implementation with the same accuracy. The present algorithm tracks, with different integration time step sizes in accordance with their different wave speeds, the propagation fronts of longitudinal and shear waves. This is accomplished by integrating separately the element-by-element partitioned longitud inal and shear equations of motion. The state vectors (displacements, velocity and accelerations) of the longitudinal and shear components are reconciled at the end of each time step. The reconciliation procedure does not require any system parameters such as material properties, density, unlike conventional artificial viscosity methods. Numerical examples are presented as applied to linear and non-linear wave propagation problems, which demonstrate high-fidelity wavefront tracking ability of the present method, and compared with existing conventional wave propagation analysis methods.

A selective mass scaling method for shear wave propagation analyses in nearly incompressible materials

“…This is the premise to apply SMS only on the wanted mode, volumetric mode in this work. Similar decomposition can be found in , where decomposition is realized modally .…”

“…For nonlinear materials, no iteration is required in the explicit method. Moreover, it is known that the implicit methods lead to the pre‐shock oscillations and the explicit methods lead to the post‐shock oscillations, see in . For wave propagation simulations, the latter case is more interesting.…”

Wave motion in a thick cylindrical rod undergoing longitudinal impact

“…In the future, the results of this paper will be used for verification of numerical methods applied to wave problems in solids [41] and for numerical dispersion studies in finite element analysis [42] and isogeometric analysis [43].…”

An Explicit Time Scheme With Local Time Stepping for One-Dimensional Wave and Impact Problems in Layered and Functionally Graded Materials

“…The nominated numerical method for wave propagation in heterogeneous materials is based on the algorithm presented by Park in [4,6]. This scheme has been reformulated into the two-time step scheme in [10]. The used time stepping process is consisted of following two computational steps for the predictor-corrector form for numerically elimination of spurious stress oscillations close to wavefront and dispersive properties of the finite element method [5] as follows: STEP 1.…”