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A LAPLACE TRANSFORM METHOD FOR THE SOLUTION OF SEMI-INFINITE AND FINITE STRIP PROBLEMS IN STRESS ANALYSIS
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1963
Year
Numerical AnalysisEngineeringMechanical EngineeringStructural OptimizationComputational MechanicsLaplace Transform MethodBoundary ConditionsMechanicsStressstrain AnalysisBoundary Element MethodMethod Of Fundamental SolutionFree Boundary ProblemSolid MechanicsPlain StrainThin-walled StructureNumerical Method For Partial Differential EquationFinite Element MethodSemi-infinite StripStructural MechanicsMechanics Of Materials
The semi-infinite strip considered extends from x = 0 to x = α. In the differential equation for the Airy stress function Φ (see (3.2)) the coordinate x is eliminated by Laplace transform. However, two of the four boundary conditions on Φ, which ought to be given at a; =0, are not known. Nevertheless they are formulated with the aid of functions with unknown parameters, in such a way that stress-singularities which may be present at the corners at x = 0, can be fully analyzed. The unknowns are determined by a special technique and further solution can be obtained in the usual manner. The method can be applied to strips loaded in or normal to their plane and to finite strips (i.e. rectangular or parallelogram-shaped plates) and to problems of plain strain in similar regions.