A new mathematical model of adhesive joint was developed and experimentally validated, in which the Vlasov–Pasternak two-parameter elastic bed model was used to simulate the stress state of the bonding layer. According to this elastic model, the adhesive layer was regarded as a membrane located in the middle of the adhesive layer thickness, between which and the bearing layers there were elastic elements. The outer bearing layers were regarded as beams in the Timoshenko approximation. The tangential stresses were considered to be constant across the thickness of the adhesive layer, and the normal (cleavage) stresses to be variable. This approach allows one to describe different types of boundary conditions for tangential stresses in the adhesive layer at the ends of the adhesive line, viz.: there are no tangential stresses at the edge of the adhesive joint if there are no adhesive spews, or the tangential stresses reach a maximum at the edge of the adhesive line if these spews exist. The problem was reduced to a system of ordinary differential equations in displacements and rotation angles of bearing layers. The system was solved by the matrix method. It was found that the sagging of the adhesive greatly reduced the maximum cleavage stresses in the adhesive layer. Tensile tests of adhesive lap-jointed metal rods were carried out. The proposed model was used to evaluate the strength criterion of the adhesive layer. It was shown that the best approximation of calculated and experimental data was provided by the maximum principal stress criterion. The proposed approach can be used to solve joint design problems.

开发了一种新的胶接接头数学模型并进行了实验验证，其中使用了Vlasov–Pasternak两参数弹性床模型来模拟粘结层的应力状态。根据该弹性模型，将粘合层视为位于粘合层厚度中间的膜，在其与支承层之间存在弹性元件。在Timoshenko近似中，外部轴承层被视为梁。切向应力被认为在整个粘合剂层的厚度上是恒定的，而法向（劈裂）应力是可变的。这种方法允许人们描述粘合线末端粘合层中切向应力的不同类型的边界条件，即：如果没有粘合剂喷出，则在粘合接头的边缘没有切向应力，或者如果存在粘合剂喷出，则在粘合剂线的边缘处的切向应力达到最大值。该问题被简化为轴承层的位移和旋转角度的常微分方程组。该系统通过矩阵法求解。发现粘合剂的流挂大大降低了粘合剂层中的最大劈裂应力。进行搭接搭接的金属棒的拉伸试验。所提出的模型用于评估粘合层的强度标准。结果表明，最大主应力准则提供了计算和实验数据的最佳近似。所提出的方法可用于解决联合设计问题。