Abstract
Plate structures are often subject to static loads that can cause the loss of strength or instability. The solution of relevant problems can be undertaken either employing equations of equilibrium or applying energy methods. This chapter illustrates the formulation and solution of representative problems for isotropic rectangular plates. While mathematical formulations presented in the chapter can be employed in a finite element or finite difference analysis, solved problems are useful either as benchmark solutions or in cases where the plate can accurately be described by the corresponding model. The chapter illustrates various boundary conditions encountered in applications and presents a discussion on their relevance. The effect of initial imperfections that are present in numerous situations is discussed in detail. The approach to the analysis of plates on an elastic foundation that is often necessary in civil engineering applications is elucidated. The analysis of stringer-reinforced plates is also included since stringers are often employed to increase the strength and stability of plates. The discussion of stability includes the peculiarities of the postbuckling response of plates that is important in numerous design applications. Besides solutions employing the integration of the equation of equilibrium, the energy (Rayleigh-Ritz) approach to the analysis is demonstrated. Although problems considered in this chapter have been studied for a long time, their value and practical applicability have not diminished. Besides the introduction to the analysis of rectangular isotropic plates, we elucidate a number of application aspects and limitations to the present solutions that are seldom discussed in textbooks on the theory of plates. This discussion may be valuable to engineers working on design and development of isotropic plate structures.
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Birman, V. (2010). Static Problems in Isotropic Rectangular Plates. In: Plate Structures. Solid Mechanics and Its Applications, vol 178. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-1715-2_2
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DOI: https://doi.org/10.1007/978-94-007-1715-2_2
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