Modeling nonlinear deformation of a plate with an elliptic inclusion by John’s harmonic material
| Autor: | Yu. V. Malkova, V. M. Malkov |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
General Mathematics
Mathematical analysis Harmonic (mathematics) 02 engineering and technology Bending of plates 01 natural sciences 010305 fluids & plasmas Nonlinear system 020303 mechanical engineering & transports 0203 mechanical engineering 0103 physical sciences Boundary value problem Tensor Constant (mathematics) Variable (mathematics) Mathematics Analytic function |
| Zdroj: | Vestnik St. Petersburg University, Mathematics. 50:74-81 |
| ISSN: | 1934-7855 1063-4541 |
| DOI: | 10.3103/s1063454117010095 |
| Popis: | The exact analytical solution of a nonlinear plane-strain problem has been obtained for a plate with an elastic elliptic inclusion with constant stresses given at infinity. The mechanical properties of the plate and inclusion are described with the model of John’s harmonic material. In this model, stresses and displacements are expressed in terms of two analytical functions of a complex variable that are determined from nonlinear boundary-value problems. Assuming the tensor of nominal stresses to be constant inside the inclusion has made it possible to reduce the problem to solving two simpler problems for a plate with an elliptic hole. The validity of the adopted hypothesis has been justified by the fact that the derived solution exactly satisfies all the equations and boundary conditions of the problem. The existence of critical plate-compression loads that lead to the loss of stability of the material has been established. Two special nonlinear problems for a plate with a free elliptic hole and a plate with a rigid inclusion have been solved. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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