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).

继早先获得的结果之后，针对圆柱弯曲的情况，构建了具有横向软芯和低横向剪切刚度和横向压缩刚度的饰面的夹心板静变形的精细非线性模型。它基于对外层挠度的厚度线性近似，对切向位移的厚度三次近似以及简化的三维弹性理论方程，可沿横向坐标进行积分，并引入两个未知函数横向软芯的厚度方向上恒定的横向切向应力。饰面的运动关系以几何非线性二次近似构造。他们允许，考虑到材料在横向剪切条件下的物理非线性行为，描述了压缩和弯曲条件下非经典的横向剪切形式的稳定性损失（FSL）。基于广义拉格朗日变分原理，构造了一维非线性方程组，通过切向位移实现了核心与饰面的平衡和共轭，从而描述了应力-应变状态（SSS）参数具有高可变性的静态变形过程）。