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 viewpoint in order that PDEs will be characterised by utilizing both means of differential geometry or algebraic geometry. this enables us to acknowledge the richness of the constitution of PDEs. It provides, for the 1st time, a geometrical thought of non-commutative (quantum) PDEs and provides a normal program of this idea to quantum box thought and quantum supergravity

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78) are insufficient to assume the calculation model's geometrical stability. To achieve this we can supplement conditions (1-78) with conditions such that u = v = 0 with f) = const (and obtain Xi = X2 = 0). The same refers to the calculation of a cylindrical shell. 7 Boundary conditions If we neglect the rods' torsion of rigidity on the plane tangential to the shell's middle surface (J21 = 0, t = 1, n), the order of the systems of differential equations describing the stressed-deformed states of the reticulated and continuous shells coincide, as well as the formulations of the problems corresponding boundary conditions.

28) becomes d2v _ d2v 2c2. 32) correspond to contours T\ and T 2 . 29) can be written as V ( r ' , )= V(T\) = 00,, (ri) V(r' V(T' (r'22)) == const, /^ It —- * — 7 == -2ir. -2ir. 33) 46 Chapter 2. 33). In accordance with the decomposition method we examine two auxiliary boundary value problems. The first auxiliary boundary value problem: d2vt g l2 = / ( ao,P)-c , / ? ) 2-,c 2 , da ~~ w,(ri) (rj) = 0. 36)

2(r (T'222)) = =const, 2:(T' v = vi V Vi = vv22..

5 from the knowledge of calculation model's stressed state. We assume that rods (i = 1,2) of the first two families are identical and omit index i(i = 1) in all designated values referring to the first family of rods, except forces and moments. The constitutive equations for shells with such a lattice have the form as Eq. 30). 33) D = [{K3c4 + K4s4)I< + K3K4/2]KK sin2 2

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