By Omri Rand

ISBN-10: 0817642722

ISBN-13: 9780817642723

This paintings makes a speciality of mathematical tools and smooth symbolic computational instruments required to unravel basic and complex difficulties in anisotropic elasticity. particular functions are provided to the category of difficulties which are encountered within the idea.

Key good points: specific emphasis is put on the choice of analytic method for a particular challenge and the opportunity of symbolic computational recommendations to aid and enhance the analytic method of problem-solving · the actual interpretation of actual and approximate mathematical options is carefully tested and offers new insights into the concerned phenomena · cutting-edge options are supplied for quite a lot of composite fabric configurations built by means of the authors, together with nonlinear difficulties and complicated research of laminated and thin-walled buildings · considerable photo examples, together with animations, extra facilitate an knowing of the most steps within the resolution approach.

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**Additional info for Analytical methods in anisotropic elasticity: with symbolic computational tools**

**Example text**

SL = S) or the case where u vanish on SD , which formally yields V ∗ = U. e. only natural boundary conditions are imposed), or in the case where zero displacements are forced over SD , one may state that: Among all stress distributions that satisfy the equilibrium equations and the natural boundary condition, those that satisfy the compatibility equations as well make the strain energy an absolute minimum. This theorem is frequently referred to as The Principle of Least Work. 8 In a state of equilibrium under the action of surface loads Fs and body force Fb , the strain energy, U, is equal to half of the work that would be done by surface and body loads (of magnitude equal to their values in the equilibrium state) by acting through the displacements from the unstressed state to the equilibrium state, namely, 2U = SL Fs · u + B Fb · u.

5 1 (a) A generic stress tensor. 5 column 1 (b) The principal stress tensor. 5: Example of a stress tensor and its principal state. 4 Two additional stress invariants, Θ4 and Θ5 (which are identical for both the stress and the stress deviator tensors) may be defined. 107) −ΘD 2 . The second invariant is defined by σDP 1 2σP2 − σP1 − σP3 √ 2 = . e. σP1 ≥ σP2 ≥ σP3 , this invariant is bounded as |Θ5 | ≤ π/6. 109) which allows graphical interpretation of Θ4 and Θ5 as presented in Fig. 6(a). 2 Visualizing the State of Stress at a Point Many visualization methods of the state of stress at a point have been discussed extensively in the literature.

128) and constitute the Theorem of Minimum Complementary Energy by stating that: Among all stress distributions that satisfy the equilibrium equations and the boundary conditions, those that satisfy the compatibility equations as well make the complementary energy an absolute minimum. 2. e. SL = S) or the case where u vanish on SD , which formally yields V ∗ = U. e. only natural boundary conditions are imposed), or in the case where zero displacements are forced over SD , one may state that: Among all stress distributions that satisfy the equilibrium equations and the natural boundary condition, those that satisfy the compatibility equations as well make the strain energy an absolute minimum.

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