Q4-Q81 - Bilinear Quadrilateral (Q4): CQUAD4 in GENESIS The...

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1 Bilinear Quadrilateral (Q4): CQUAD4 in GENESIS The displacement field in terms of generalized coordinates: So, u and v fields are bilinear in x and y (i.e., product of two linear polynomials). Because of form, sides are stiffer than diagonals-artificial anisotropy! The Q4 element has four nodes and eight nodal dof. The shape can be any quadrilateral ; we’ll concentrate on a rectangle now .
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2 Q4: The strain fields The strain field in the element: Observation 1: ε x f(x) Q4 cannot exactly model the following beam where ε x x
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3 Q4: Behavior in Pure Bending of a Beam Observation 2: When β 4 0, ε x varies linearly in y and γ xy 0. The former is a desirable characteristic of Q4 if a beam in pure bending is to be modeled because normal strain varies linearly along the depth coordinate of a beam in pure bending but γ xy 0 is undesirable because there is no shear strain. Fig. (a) is the correct deformation in pure bending while (b) is the deformation of Q4 (the sides remain straight ). Physical interpretation: applied moment is resisted by a spurious
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This note was uploaded on 06/06/2011 for the course EAS 4240 taught by Professor Peterifju during the Spring '08 term at University of Florida.

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Q4-Q81 - Bilinear Quadrilateral (Q4): CQUAD4 in GENESIS The...

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