Introduction to the Theory of Plates - Stanford （介绍板的理论斯坦福大学）.pdfVIP

Introduction to the Theory of Plates /~chasst/Course%20Notes/PlatesBook... Introduction to the Theory of Plates Charles R. Steele and Chad D. Balch Division of Mechanics and Computation Department of Mecanical Engineering Stanford University Stretching and Bending of Plates - Fundamentals Introduction A plate is a structural element which is thin and flat. By “thin,” it is meant that the plate’s transverse dimension, or thickness, is small compared to the length and width dimensions. A mathematical expression of this idea is: where t represents the plate’s thickness, and L represents a representative length or width dimension. (See Fig. See Plate and associated (x, y, z) coordinate system...) More exactly, L represents the minimum wave length of deformation, which can be much smaller than the plate minimum lateral dimension for problems of localized loading, dynamics and stability. Plates might be classified as very thin if Łt 100, moderately thin if 20 Łt 100, thick if 3 Łt 20, and very thick if Łt 3. The “classical” theory of plates is applicable to very thin and moderately thin plates, while “higher order theories” for thick plates are useful. For the very thick plates, however, it becomes more difficult and less useful to view the structural element as a plate - a description based on the three-dimensional theory of elasticity is required. 1 of 41 4/2/09 2:20 PM Introduction to the Theory of Plates /~chasst/Course%20Notes/PlatesBook... FIGURE 1.1. Plate and associated (x, y, z) coordinate system. In this chapter, we derive the basic equat