Plate Stability by Boundary Element Method

ISBN-13: 9783540537106 / Angielski / Miękka / 1991 / 205 str.

Abbas Elzein; A. Elzein

Opis

1. 1 Historical Background Thin plates and shells are widely used structural elements in numerous civil, mechanical, aeronautical and marine engineering design applications. Floor slabs, bridge decks, concrete pavements, sheet pile retaining walls are all, under normal lateral loading circumstances, instances of plate bending in civil engineering. The problem of elastic instability of plates occurs when load is applied in a direction parallel to the plane of the plate. The deck of a bridge subjected to a strong wind loading, the web of a girder under the action of shear forces transmitted by the flanges, the turbine blade of a machinery undergoing longitudinal temperature differentials, would all eventually buckle when the applied load, or its temperature equivalent in the last case, exceeds a certain limit, that is the buckling load. Although the plate may exhibit a considerable post-buckling strength, the buckling load is considered in many design instances, especially in aeronautical and marine engineering, as a serviceability limit because of the abrupt and substantial change in the dimensions and shape of the buckled plate. Nevertheless, the post-buckling region retains its importance either as an essential safety margin or as a stage of loading actually reached under normal loading conditions. The design engineer will therefore need rigorous tools of analysis to predict, in addition to the buckling load, the deflections and stresses at both buckling and initial post-buckling stages.

Spis treści

1 Introduction.- 1.1 Historical Background.- 1.2 Stability.- 1.3 Experimental and Numerical Modelling.- 1.4 The Boundary Element Method.- 1.5 Plate Stability by BEM.- 1.6 Scope of the Present Work.- 2 Plate Stability Theory.- 2.1 Introduction.- 2.2 Stability of Structural Systems.- 2.3 Linear Theory.- 2.4 Large Deflections.- 2.5 Boundary Conditions.- 2.5.1 Out-of-Plane Boundary Conditions.- 2.5.2 In-Plane Boundary Conditions.- 2.6 Numerical and Experimental Studies.- 2.7 Conclusions.- 3 Membrane State of Stress.- 3.1 Introduction.- 3.2 Boundary Integral Formulation.- 3.3 Boundary Element Solution.- 3.4 Numerical Implementation.- 3.5 Results.- 3.6 Conclusions.- 4 Critical Loads.- 4.1 Introduction.- 4.2 Boundary Integral Formulation.- 4.3 Boundary Element Solution.- 4.3.1 Modelling of Boundary Unknowns.- 4.3.2 Domain Deflection Models.- 4.3.2.1 Continuous Cells.- 4.3.2.2 Discontinuous Cells.- 4.3.3 Free Boundary.- 4.3.4 Eigenvalue Problem.- 4.4 Numerical Implementation.- 4.5 Results.- 4.5.1 Optimum Nodal Position in Discontinuous Elements.- 4.5.2 Performance of the Various Interpolation Models.- 4.5.3 Convergence of Results from the Linear Discontinuous Model.- 4.5.4 Comparison with Exact Solutions.- 4.5.5 Comparison with the Finite Element Method.- 4.6 Conclusions.- 5 Dual Reciprocity.- 5.1 Introduction.- 5.2 Outline of the Method.- 5.3 The Discrete Points Fourier Analysis.- 5.3.1 The One-Dimensional Fourier Series.- 5.3.2 The Two-Dimensional Fourier Series.- 5.3.3 The Discrete Points Two-Dimensional Fourier Analysis.- 5.4 The Deflection Models.- 5.4.1 The Trigonometric Deflection Model.- 5.4.2 The Nodal Deflection Model.- 5.5 Transformation of L(w).- 5.6 Transformation of the Domain Integral.- 5.7 The Problem of Singular Integrals.- 5.8 Eigenvalue Problem.- 5.9 Numerical Implementation.- 5.10 Results.- 5.10.1 Convergence of the Fourier Transformation.- 5.10.2 Convergence of the Transformed Integrals.- 5.10.3 Examples of Critical Loads.- 5.10.3.1 The Trigonometric Deflection Model.- 5.10.3.2 The Nodal Deflection Model.- 5.10.3.3 The Plates Deflected Shape.- 5.11 Conclusions.- 6 Large Deflections.- 6.1 Introduction.- 6.2 Boundary Integral Formulation.- 6.3 Domain Deflection Models.- 6.4 Boundary Element Solution.- 6.5 Solution of the System of Equations.- 6.6 Numerical Implementation.- 6.7 Results.- 6.8 Conclusions.- 7 Conclusions.- Appendix A The Green’s Identities.- Appendix B Functions of the Fundamental Solutions.- Appendix C Trigonometric Deflection Functions.- References.