The authors propose a mathematical model of shell structures taking into account the linear theory of hereditary material creep. This model is based on the total potential strain energy functional. Shells are reinforced with stiffeners, and the contact between the stiffener and the shell skin along a strip is taken into account. The Ritz method is applied to the functional, and a system of algebraic or integro-algebraic equations is found. The resulting system is first solved as a linear system (without account for the terms reflecting material creep), and the state of the structure under the specified load is determined. Then the iterative method is used to solve the creep problem for a given value of time. The paper presents the results of studying stiffened shallow shells of double curvature made of reinforced concrete under uniformly distributed load. The buckling of shells occurs over time as a result of the development of creep strains. Values of the buckling load as a result of material creep are found. It is shown that stresses are redistributed over the shell field over time and the maximum stress is observed near the contour of the structure.

作者提出了一种考虑遗传材料蠕变线性理论的壳结构数学模型。该模型基于总势应变能泛函。壳体采用加劲肋加固，并考虑加劲肋与壳体蒙皮沿条带的接触。将 Ritz 方法应用于泛函，并找到代数或积分代数方程组。所得系统首先作为线性系统求解（不考虑反映材料蠕变的术语），并确定结构在指定载荷下的状态。然后使用迭代方法求解给定时间值的蠕变问题。本文介绍了在均匀分布载荷下由钢筋混凝土制成的双曲率加筋浅壳的研究结果。由于蠕变应变的发展，随着时间的推移，壳会发生屈曲。找到材料蠕变导致的屈曲载荷值。结果表明，随着时间的推移，应力在壳场上重新分布，并且在结构轮廓附近观察到最大应力。