A Theory of Elasticity with Microstructure for Directionally by J.D. Achenbach

By J.D. Achenbach

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W h ere ui midflane of the kth reinforcing and kth matrix layer, respectively. r,(fk) ¥'21 1/122 (fk) represents symmetric thickness stretch deformation of the kth reinforcing layer. Analogous definitions apply to 1/12\me) , 1/123 (me) and 1/l~nk) . Thus the displacements in a layers are expressed as the displacements in the midplane plus additional terms which increase linearly with the distance from the midplane. Note 1/12 /me) are defined at discrete values of x 2 , but they are that iii (fk) , iii (me), continuous functions of x 1 , x 3 and t.

7 )-( 1. 9), the Greek indices a:: and f) can assume the values 1 or 3 only. By replacing superscripts f by superscripts m in Eqs. ( 1. 7 )-( 1. 9) the corresponding expressions for the strain components in the kth matrix layer are obtained. Substitution of the expressions (1. 7 )-( 1. 9) into Eq. Lfll . Nk>Y+(a31j12~k>Y] A similar computation yields an expression for the strain energy stored in an element of unit surface area of the kth matrix layer. The actual expression for W (mk) can be written by replacing in Eq.

Are given by Eqs. 11), respectively. 13b) are uncoupled wave equations. p and the vector potential with components 1/li are generally coupled through the boundary conditions, which still causes substantial mathematical complications, the use of the displacement decomposition generally simplifies the analysis. To determine the solution of a boundary-initial value problem one may simply select appropriate particular solutions of Eqs. 13b) in terms of arbitrary functions or integrals over arbitrary functions.

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