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Discrete Gradient Method in Solid Mechanics
A discrete method without element and shape function
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The discrete gradient method is proposed as a novel numerical tool to perform solid mechanics analysis directly on point-cloud models without converting the models into a finite element mesh. This method does not introduce continuous approximation of the primary unknown field variables; instead, it computes the gradients of the field variables at a node using discrete differentials involving a set of neighboring nodes. Therefore, the formulation renders a completely discrete computation that can conduct mechanical analysis on point-cloud representations of patient- specific organs without resorting to finite element method.
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