A theory of latticed plates and shells by G I Pshenichnov

By G I Pshenichnov

This quantity offers the speculation of partial differential equations (PDEs) from a contemporary geometric standpoint in order that PDEs may be characterised through the use of both means of differential geometry or algebraic geometry. this permits us to acknowledge the richness of the constitution of PDEs. It offers, for the 1st time, a geometrical conception of non-commutative (quantum) PDEs and provides a basic software of this idea to quantum box concept and quantum supergravity

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101) 38 Chapter 1. 99) into account. Note that the constitutive Eqs. 22) with J 2 ; = 0 and the lattice's stable parameters with the main terms of effective characteristics for simple frameworks resulting from averaging processes in periodic media [6], [18], [24]. 1 Solution of Equations and Boundary Value Problems by the Decomposition Method Decomposition method This method was suggested in the work [49] and the basis of it is contained in the following. , j/ m (x)} of the boundary value problem Li{y) = fi(x), WV) /<(*).

2. sinx ^sinx rsinx = e'i sin Acos0 — u/cos A cos 5 + e'2cos A sin 9, = K' «'iI sin 2 0 + T'COS(A — 9) + /c'2sin2 A, = — "i sin 0 cos 0 — r'sin(A — 9) + /c'2sin A cos A, K2 sin x = K'I cos COS22 9 — — T' COS(A — 6) 9) + + K'22 COS cos2 A (deformation components for the oblique-angled system of coordinates are primed) may be presented in the following constitutive equations: JVf'Wx = CPZ c ^ + +c ^ + cpV JV<'>sin2x = CJP^+CJpu/ (j 22 A/^ >sin M sin x = (i M), (i = =M ), -(D^K^ -(D[ K\ K[ + + D^K^ D< V2 + + D^T Z ) 3 V)) J) ; J 1 (j =T~i).

A b The linear system of algebraic equations was solved using the Gaussian method with columnwise pivoting. Calculations were performed on three grids with division of the rectangular domain's sides in 2, 4 and 8 parts (N = M = 1, 3, 7 respectively) for the domains with the b/a sides' relationship 1 and 3. In all cases relative errors > {^ ¥) T T- \uiP-u,\ max J —rj—.

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