A mathematical model of viscoelastic-plastic bending deformation of spatially reinforced plates is developed based on the time step method. The viscoelastic behavior of the components of the composition is described by the Maxwell-Boltzmann equations, and plastic behavior by flow theory with isotropic hardening. The low resistance of composite plates to transverse shear is taken into account within the framework of Reddy’s theory, and the geometric nonlinearity of the problem is considered in the von Kármán approximation. The corresponding initial-boundary-value problem is solved using a leapfrog numerical scheme. The dynamic viscoelastic-plastic bending of spatially reinforced fiberglass rectangular plates subjected to air blast wave loading is investigated. It is shown that for relatively thick plates, replacing a flat reinforcement structure by a spatial reinforcement structure leads to a significant decrease in the maximum and residual deflections and strain intensity of the binder material, and for relatively thin plates, this replacement is ineffective. It is found that in the initial stage of deformation, the amplitude of oscillation of the composite plate far exceeds the residual deflection.

中文翻译：

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粘弹性 - 具有空间钢筋结构的板的塑性变形

基于时间步长方法建立了空间增强板粘弹塑性弯曲变形的数学模型。组合物组分的粘弹性行为由麦克斯韦-玻尔兹曼方程描述，塑性行为由具有各向同性硬化的流动理论描述。在 Reddy 理论的框架内考虑了复合板对横向剪切的低阻力，并在 von Kármán 近似中考虑了问题的几何非线性。相应的初始边界值问题是使用跳蛙数值方案解决的。研究了受到空气冲击波载荷的空间增强玻璃纤维矩形板的动态粘弹塑性弯曲。结果表明，对于较厚的板，用空间增强结构代替平面增强结构会导致粘结材料的最大和残余挠度和应变强度显着降低，对于相对薄的板，这种替换是无效的。发现在变形初期，复合板的振荡幅度远远超过残余挠度。