Abstract

Explicit dynamic analysis has proven to be advantageous when simulating shock and impact loading, and very small time-scale events. In this article, the potential for using B-spline elements for explicit dynamic simulation is studied. An isoparametric formulation is presented for quadratic and cubic elements and their shape functions are derived from the classical recursive definition of B-splines. Step boundary method, which uses the equations of the boundary to construct trial functions, is used for imposing boundary conditions. Its suitability for analysis using a uniform B-spline element mesh that does not conform to the geometry and its applicability to explicit dynamic simulation are examined in this article. Furthermore, the effectiveness of mass diagonalization for B-Spline elements is also explored. This approach is validated using several examples by comparing with modal superposition solutions as well as past work and analytical solutions when available.

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