* entire textbook/reference applies mathematical equipment and smooth symbolic computational tools to anisotropic elasticity * Presents unified method of an enormous range of structural versions * state of the art recommendations are supplied for a variety of composite fabric configurations, together with: 3-D anisotropic our bodies, 2-D anisotropic plates, laminated and thin-walled constructions

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Extra info for Analytical Methods in Elasticity

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215)), and their respective areas are Ai = H j Hk dα j dαk (apply cyc-i jk). The areas of the corresponding faces after deformation are denoted A∗i . Based on the above definitions, the forces that act over faces #1,2 and 3 may be written as A∗ A∗i σ i (i ∈ {1, 3}), or, equivalently, Ai σ i H j Hk dα j dαk . We will now decompose σ i along the i deformed and the undeformed directions, respectively, as σ i = ∑ j=1 σi j kˆ ∗j , 3 It may be verified that A∗i 3 σ i = ∑ j=1 si j kˆ j . Ai ⎧ ⎫ ⎧ ⎫ ⎨ σi1 ⎬ ⎨ si1 ⎬ si2 = [I + e + ω ] σi2 , ⎩ ⎭ ⎩ ⎭ σi3 si3 i = 1, 2, 3.

Hence, the discussion regarding the stress tensor is applicable in a direct manner by replacing σi j with εi j , etc. Subsequently, a matrix Mε = Mσ may be defined, and the strain tensor invariants Ξ1 , Ξ2 , Ξ3 , the eigenvalues εPi and the principal axes may be calculated analogously. 3. 12 for visualization of a state of strain at a point. 11 executes transformations of a strain tensor between curvilinear and Cartesian coordinates. 4 Energy Theorems In this section we shall review some work- and energy-based measures that are encountered in the theory of elasticity.

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. In view of the powerful modern visualization tools, the classical methods seem less attractive and important. We will describe the main ideas in this area briefly. A good starting point is the examination of the stresses over a face of an infinitesimal cube having general orientation so that the normal to the face under discussion is oriented at the x direction as shown in Fig.