Principle of complementary virtual work and the Riemann-Christoffel curvature tensor as compatibility condition (Q2714414)
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scientific article; zbMATH DE number 1604338
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Principle of complementary virtual work and the Riemann-Christoffel curvature tensor as compatibility condition |
scientific article; zbMATH DE number 1604338 |
Statements
13 June 2001
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nonlinear kinematics of deformation
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principle of complementary virtual work
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compatibility field equations
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stress tensor
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Ricci tensor
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Riemann-Christoffel tensor
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Cauchy deformation tensor
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Green deformation tensor
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0.8577986
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0.83803767
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0.8203095
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0.81026787
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0.80328923
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Principle of complementary virtual work and the Riemann-Christoffel curvature tensor as compatibility condition (English)
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In nonlinear solid mechanics it is well known that from the principle of complementary virtual work one can derive the compatibility field equations (CFE) if the stresses are given by means of a stress function tensor which guarantees equilibrium. In this paper it is shown that the CFE are equivalent to the zero-valuedness of Ricci as well as Riemann-Christoffel curvature tensors in the current and reference configurations respectively, where the changed metric tensors are expressed in terms of Cauchy and Green deformation tensors respectively.
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