In this chapter, we discuss the transition from the three-dimensional problem of elasticity theory with initial stresses in a thin layer to two-dimensional problem of plate theory in the case when the initial stresses are of the same order as the elastic constants of the material of the plate. The initial stresses cannot exceed the strength of the material(s), which does not exceed a few percent of Young’s modulus of the material(s), see Sect. 4.5, in particular Table 4.1. Thus, the initial stresses are much smaller than the elastic constants in absolute value.

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Initial Stresses Comparable to the Elastic Constants of the Material of the Plate

  • Alexander Kolpakov

摘要

In this chapter, we discuss the transition from the three-dimensional problem of elasticity theory with initial stresses in a thin layer to two-dimensional problem of plate theory in the case when the initial stresses are of the same order as the elastic constants of the material of the plate. The initial stresses cannot exceed the strength of the material(s), which does not exceed a few percent of Young’s modulus of the material(s), see Sect. 4.5, in particular Table 4.1. Thus, the initial stresses are much smaller than the elastic constants in absolute value.