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Basic Theory of Plates and Elastic Stability - Part 1

Tài liệu tham khảo giáo trình cơ học kết cấu trong ngành xây dựng bằng Tiếng Anh - Yamaguchi, E. “Basic Theory of Plates and Elastic Stability” Structural Engineering Handbook Ed. Chen Wai-Fah Boca Raton: CRC Press LLC, 1999 - Basic Theory of Plates and Elastic Stability | Yamaguchi E. Basic Theory of Plates and Elastic Stability Structural Engineering Handbook Ed. Chen Wai-Fah Boca Raton CRC Press LLC 1999 Basic Theory of Plates and Elastic Stability Eiki Yamaguchi Department of Civil Engineering Kyushu Institute of Technology Kitakyusha Japan 1.1 Introduction 1.2 Plates Basic Assumptions Governing Equations Boundary Conditions Circular Plate Examples of Bending Problems 1.3 Stability Basic Concepts Structural Instability Columns Thin- Walled Members Plates 1.4 Defining Terms References Further Reading 1.1 Introduction This chapter is concerned with basic assumptions and equations of plates and basic concepts of elastic stability. Herein we shall illustrate the concepts and the applications of these equations by means of relatively simple examples more complex applications will be taken up in the following chapters. 1.2 Plates 1.2.1 Basic Assumptions We consider a continuum shown in Figure 1.1. A feature of the body is that one dimension is much smaller than the other two dimensions t Lx Ly 1.1 where t Lx and Ly are representative dimensions in three directions Figure 1.1 . If the continuum has this geometrical characteristic of Equation 1.1 and is flat before loading it is called a plate. Note that a shell possesses a similar geometrical characteristic but is curved even before loading. The characteristic of Equation 1.1 lends itself to the following assumptions regarding some stress and strain components ơz 0 1.2 z xz yz 0 1.3 We can derive the following displacement field from Equation 1.3 1999 by CRC Press LLC FIGURE 1.1 Plate. u x y z u- x y - z -@x v x y z VQ x y - z -@y w x y z w- x y 1.4 where u V and w are displacement components in the directions ofx- y- and z-axes respectively. As can be realized in Equation 1.4 UQ and VQ are displacement components associated with the plane of z Q. Physically Equation 1.4 implies that the linear filaments of the plate initially perpendicular to the middle surface remain straight and .