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On the application of Lagrange multipliers to statics problems of composite shells. (Ukrainian) Zbl 0937.74042

A version of the shell theory is constructed, in which deformations of the smaller order are used as additional solving functions. The advantage of the suggested approach is as follows. Under insignificant increase of the volume of calculations, one has a more algorithmic approach both to the derivation of governing equations and to their numerical solution. It is unnecessary to calculate transverse forces in physically nonlinear problems, since they are Lagrange multipliers and are determined automatically. For geometrically nonlinear shell theory one can consider large shell deflections more simply as there is no necessity to express angles of the rotation of normal through displacement. The author considers a test problem and demonstrates good convergence of the suggested technique.

MSC:

74K25 Shells
74S30 Other numerical methods in solid mechanics (MSC2010)
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