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Critical Time-Step Estimation for Explicit Integration of Dynamic Higher-Order Finite-Element Formulations
AbstractHigher-order elements frequently render accurate results and allow the reduction of the total number of elements required to represent a given structure. However, element order also affects the efficient time-history integration of the associated equations of motion in Lagrangian dynamics by an explicit method, which is only conditionally stable. The integration time step is affected by element type and must be sufficiently small to avoid instability of the computed solution and, simultaneously, should be sufficiently large for an economic analysis. The upper bound to the size of this step in an analysis is rigorously obtained from the solution of the eigenvalue problem to the global system of equations of the entire finite-element model. Common alternatives to this computation are to approximate the time step by much simpler one-dimensional node-to-node or individual elemental eigenvalue approaches. Robust higher-order finite-element formulations have recently been developed for explicit integration, but time-step determinations have been primarily limited to the one-dimensional approach. In this paper, the individual elemental eigenvalue approach is further used to study the critical time step for several practical higher-order element types (27-node bricks, 16-node thin plates, 15-node tetrahedra, and 21-node wedges). Parametric studies on the variables controlling their critical time steps are discussed.
Critical Time-Step Estimation for Explicit Integration of Dynamic Higher-Order Finite-Element Formulations
AbstractHigher-order elements frequently render accurate results and allow the reduction of the total number of elements required to represent a given structure. However, element order also affects the efficient time-history integration of the associated equations of motion in Lagrangian dynamics by an explicit method, which is only conditionally stable. The integration time step is affected by element type and must be sufficiently small to avoid instability of the computed solution and, simultaneously, should be sufficiently large for an economic analysis. The upper bound to the size of this step in an analysis is rigorously obtained from the solution of the eigenvalue problem to the global system of equations of the entire finite-element model. Common alternatives to this computation are to approximate the time step by much simpler one-dimensional node-to-node or individual elemental eigenvalue approaches. Robust higher-order finite-element formulations have recently been developed for explicit integration, but time-step determinations have been primarily limited to the one-dimensional approach. In this paper, the individual elemental eigenvalue approach is further used to study the critical time step for several practical higher-order element types (27-node bricks, 16-node thin plates, 15-node tetrahedra, and 21-node wedges). Parametric studies on the variables controlling their critical time steps are discussed.
Critical Time-Step Estimation for Explicit Integration of Dynamic Higher-Order Finite-Element Formulations
Danielson, Kent T (author) / de Béjar, Luis A
2016
Article (Journal)
English
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