By Omri Rand

This paintings makes a speciality of mathematical tools and smooth symbolic computational instruments required to resolve basic and complicated difficulties in anisotropic elasticity. particular functions are awarded to the category of difficulties which are encountered within the concept.

Key good points: specific emphasis is put on the choice of analytic technique for a selected challenge and the possibility of symbolic computational recommendations to aid and strengthen the analytic method of problem-solving · the actual interpretation of actual and approximate mathematical options is punctiliously tested and gives new insights into the concerned phenomena · cutting-edge recommendations are supplied for quite a lot of composite fabric configurations built by way of the authors, together with nonlinear difficulties and complicated research of laminated and thin-walled buildings · considerable picture examples, together with animations, extra facilitate an figuring out of the most steps within the answer method.

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**Example text**

110b), σT as described by the surface in Fig. 10(a) is obtained. One may also create a three-dimensional (spherical) surface of σN = σ11 (θ, ψ), and σT = σ212 (θ, ψ) + σ213 (θ, ψ). 12 and replace ψ by θs and θ by φs − π2 , respectively, where θs and φs are spherical angles, see Fig. 20(b). These spherical plots are shown in Figs. 10(b) where each point on the surface represents an orientation of the x-axis of the transformed system (by connecting the origin with it). Thus, σN and σT are directly proportional to the distance that is measured along the x-axis between the origin and the corresponding surfaces.

130) As a special case of the above theorem, we may consider two discrete surface loads acting over points A and B of an elastic body, and suppose that no body forces are applied. When the force Fs (A) (at A) is applied, the displacements uAA at A and uAB at B are obtained. When the force Fs (B) (at B) is applied, the displacements uBA at A and uBB at B are obtained. 131) Fs (A) · uBA = Fs (B) · uAB . 131) shows that αAB = αBA . 4 Castigliano’s Theorems We shall now examine the case of the Theorem of Minimum Potential Energy, where body forces are absent and the surface loading Fs k (k = 1, .

One may also create a three-dimensional (spherical) surface of σN = σ11 (θ, ψ), and σT = σ212 (θ, ψ) + σ213 (θ, ψ). 12 and replace ψ by θs and θ by φs − π2 , respectively, where θs and φs are spherical angles, see Fig. 20(b). These spherical plots are shown in Figs. 10(b) where each point on the surface represents an orientation of the x-axis of the transformed system (by connecting the origin with it). Thus, σN and σT are directly proportional to the distance that is measured along the x-axis between the origin and the corresponding surfaces.