Download A theory of latticed plates and shells by G I Pshenichnov PDF

By G I Pshenichnov

This quantity offers the speculation of partial differential equations (PDEs) from a latest geometric perspective in order that PDEs could be characterised by utilizing both means of differential geometry or algebraic geometry. this permits 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 offers a common program of this idea to quantum box concept and quantum supergravity

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Additional info for A theory of latticed plates and shells

Example text

0* = 0,c, + 0 2 s t ; V. 17); 8U 62— are the mean curve angles of the normal in planes /? = const and a = const. 16). , = -±S-^M; u222 = ±i * A :, M -E is"*" ■K, 5 = t=i 1=1 a —v S,Cj aa ■ i=l i ==i i '' aa i=l ,=i < n S s i=l i=i 1=1 aa < «> ==E±fQh Qx ^ ; . 99) <—i These formulae disregard the rods' torsional rigidity and bending in the plane tangent to the shell's middle surface. 2 Allowance for the rods' non-linear-elastic deformation We now obtain constitutive equations in the reticulated shell theory when the rods' material is non-linearly elastic.

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.. 37) can be solved using various known methods. ) is expanded into a series according to a certain system of linearly independent basis functions in the domain limited by contours T\ and T2.

This assures a high rate of convergence. When using numerical methods for solving the problems, functions /*(x) are taken as the basic unknown ones. The grid approximation of these functions guarantees a high accuracy of results on rather sparse grids. 2) may not only be differential operators, but also more general operators. 1a. Precise solution of a non-linear differential equation with partial derivatives. 9) where a, b are constants. We introduce two equations (2au1 + bxy)du dui1/dx+ Idx 4 byui (2au22 + + bxy)du y)du2/dy + - bxu2 = f{x,y) + + qi(x), = -f{x, y) + q2(y).

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