Article
MSC:
35K05,
49J40,
73K10,
73U05,
74A15,
74F05,
74H45,
74K20,
74S05,
80A20 | MR 0678110 | Zbl 0506.73012 | DOI: 10.21136/AM.1982.103987
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Keywords:
nonlinear dynamical; kinematical; linear constitutive thermoelastic; coupled heat conduction equations; spatial problem; Kirchhoff’s and von Kármán’s hypothesis; twodimensional equations; generalized problem with subgradient conditions on boundary; existence of solution; continuous dependence on given data
nonlinear dynamical; kinematical; linear constitutive thermoelastic; coupled heat conduction equations; spatial problem; Kirchhoff’s and von Kármán’s hypothesis; twodimensional equations; generalized problem with subgradient conditions on boundary; existence of solution; continuous dependence on given data
Summary:
The vibration problem in two variables is derived from the spatial situation (a plate as a three-dimensional body) on the basis of geometrically nonlinear plate theory (using Kármán's hypothesis) and coupled linear thermoelasticity. That leads to coupled strongly nonlinear two-dimensional equilibrium and heat conducting equations (under classical mechanical and thermal boundary conditions).
For the generalized problem with subgradient conditions on the boundary and in the domain (including also classical conditions), existence and dependence of the weak variational solution on the given data is proved.
References:
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