By G I Pshenichnov
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Extra info for A theory of latticed plates and shells
19) provides the following two additional boundary conditions: Mu = M22a. = 0 at Mi, 0 = 00Oa. 79) 2. The rods are rigidly hinged along the contour: the turn angles of the two families of rods around the normal to the shell's middle surface on its contour are equal. Besides, the linear bending moment at the plane tangential to the shell's middle surface has a preset value on the contour. 80) where M°,(a) is a preset function. 0. 12). 80) is homogeneous) is shown in Fig. 8b. 3. More Precise Constitutive Equations 33 3.
68) it follows that one of the shell's longitudinal cross sections need to have connections preventing displacements of the middle surface points along its generatrices. Here we assume u = 0 (a = = const). 69) The condition u = 0 can be replaced by u = const, and v = 0 by v = const. This would result in the calculation model's possible displacement as a rigid entirety. 2. Constitutive Equations tp = C\ cos/? — C2sinP + Cs. 66) we find that ip = 0. 68) C\ = C2 = 0. a,uaa22));; (a == Qi,a (Q Qi,a22);); 0 00 00 00 00 00 = ct\); ai); ((a = a = a up a,,/?
77) Thus, if the calculation model is unfixed it is geometrically changeable. Let a portion of boundary conditions expressing the fastening of the shell's transversal edges, have the from v = (T? ), =w w= = 00 (r? 78) where n. = (/ tan tp)/R, I is the shell's length. 77) we must assume 01 = Xl Xi + X2, 02 = "Xi -Xi + X2, C, = 0 (2 (i = 175), 1,5), where xi, X2 are arbitrary periodical odd and even functions with period 2r]'. 76) takes the form « = \Xi(l + P)-xAv-P) •ifo-/») + X7(ri + 0) + X7(ri-P)]tan
A theory of latticed plates and shells by G I Pshenichnov