DifferentialEquations_03_Compatibility - Section 1.3 1.3...

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Section 1.3 Solid Mechanics Part II Kelly 17 1.3 Compatibility of Strain As seen in the previous section, the displacements can be determined from the strains through integration, to within a rigid body motion. In the two-dimensional case, there are three strain-displacement relations but only two displacement components. This implies that the strains are not independent but are related in some way. The relations between the strains are called compatibility conditions . 1.3.1 The Compatibility Relations Differentiating the first of 1.2.5 twice with respect to y , the second twice with respect to x and the third once each with respect to x and y yields + = = = y x u y x u y x y x u x y x u y y x xy y yy x xx 2 3 2 3 2 2 3 2 2 2 3 2 2 2 1 , , ε It follows that y x x y xy yy xx = + 2 2 2 2 2 2 2-D Compatibility Equation (1.3.1)
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DifferentialEquations_03_Compatibility - Section 1.3 1.3...

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