Nonlinear integro-differential equations of bending of physically nonlinear viscoelastic plates

Abstract An important feature of real materials is the nonlinear nature of the relationship between stress and strain. Taking into account such features of deformation of structural materials in the calculation allows us to bring theoretical forecasts closer to their real behavior. Physical nonlinearity is due to the calculation in the calculation of the nonlinear dependence between the components of the generalized stresses and strains characterizes the work of the structural material in the elastoplastic region. Many structural elements of modern technology are made in the form of plates of various shapes. The widespread use of plates is explained by their high strength, considerable rigidity and relatively low weight, which, along with the manufacturability of manufacturing, distinguishes them among other structural elements. A constant trend in the development of technology is an increase in the intensity of dynamic effects, accompanied by an increase in the level of vibration.

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