The work considers numerical solution of problems of static bending and steady-state vibrations of thin rectangular plates and shells under local loads specified by functions of a special type. The approach is applied to solving problems for plates of isotropic, orthotropic and viscoelastic material and isotropic cylindrical shells. The results are compared to known theoretical solutions and the results obtained by other numerical methods. Considering cylindrical shells, the results obtained for classical theory are compared with those for flat shell theory and the conclusion about the correctness of the hypothesys of flat shell theory is made.
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