Mathematical Modelling in Thermomechanics of Elastic Shells by Iterative-Moment Approach - Zozulyak, Y. (Фізико-математичне моделювання та інформаційні технології, 2006)
General approaches to mathematical modelling of thermomechanical processes in thin-walled elements of plate and shell type in a three-dimensional approximation are discussed. The energy balance equation, formulated in a three-dimensional statement by Lagrange approach on the extended space of parameters of local state and a corresponding choice of the function of local situation is the basis for the construction of governing equations. In this connection the mechanic energy flow, in a general case, is given by a sum of additive components in which apart of traditional characteristics (stress tensor, velocity vector) the higher order characteristics of gradientality of deformation and inertial motion and corresponding to them tensor characteristics of force action are introduced iteratively. The set of governing equations enabling to account the effects of locally-gradient and high-speed deformations was constructed for determination of the phase space of parameters of local situation. The transition to a two-dimensional analogue in governing equations is realized by the averaged characteristics of the stressed-strained state using presentation of the sought-for values by means of the expansion by a tensor base.