4/1/08 EP 471 -- Engineering Problem Solving II Exercise 15 Gaussian Quadrature and Work Equivalence in Finite ElementsIn EMA 405, we typically look at a few idealized problems where we convert a continuous load distribution into an equivalent discrete load set. Focusing now on eight-node quads, we can perform integrations in 2D problems that convert body forces to discrete loads or in 3D problems that convert surface tractions to discrete loads (8-node quads are the surfaces of 20-node hexahedral elements). One of our results is that for square elements, a constant pressure exerted on an 8-node quad produces a work-equivalent load set equal to -1/12 ×pAon the corner nodes and +1/3 ×pAon the midside nodes, where F= pAis the total resultant force on the face of the element (pressure ×surface area). The form of the conversion produces force on node iequal to: ηξηξηξddJfpFiidet),(),(1111∫ ∫+−+−=Here pis the distributed load on the surface (constant for uniform pressure), fi
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