В издательстве Springer опубликована научная работа ассистента кафедры вычислительной математики Макарова М.В.
Paimushin V.N., Makarov M.V., Polyakova N.V. Refined Nonlinear Deformation Model of Sandwich Plates with Composite Facings and Transversal-Soft Core // Russian Mathematics. – 2020. – V. 64, No. 11 – P. 83–89. https://doi.org/10.3103/S1066369X20110080
Following up on the results obtained earlier, a refined nonlinear model of static deformation of sandwich plates with transversal-soft core and facings with low stiffness of transverse shear and transverse compression is constructed for the case of cylindrical bending. It is based on the use of linear approximations in thickness for deflections of the external layers, cubic approximation in thickness for tangential displacements, and simplified three-dimensional equations of elasticity theory that can be integrated along the transverse coordinate with introduction of two unknown functions representing constant transverse tangential stresses in thickness for transversal-soft core. The kinematic relations for the facings are constructed in a geometrically nonlinear quadratic approximation. They allow, taking into account physical nonlinear behavior of the material under transverse shear conditions, the description of non-classical transverse-shear forms of stability loss (FSL) in both compression and bending conditions. Based on the generalized Lagrange variational principle, one-dimensional nonlinear equations of equilibrium and conjugation of the facings with the core by tangential displacements are constructed to describe the static deformation process with high rates of variability of the parameters of the stress-strain state (SSS).