Analysis of beam with thin open sections as cylindrical shells evidences restrictions of the Wagner-Vlasof theory: these mainly concern the fulfillment of end conditions. For the case of large deflections, the resultant equations from asymptotic analysis are presented. Their application to buckling under pure flexure shows various novel aspects. By a simple direct approach, investigation is pursued beyond the critical state: the buckled configuration turns out to be stable even for laxer constraints...
A numerical accuracy test for finite element or finite difference methods in linear shell problems is suggested.
Analysis of beam with thin open sections as cylindrical shells evidences restrictions of the Wagner-Vlasof theory: these mainly concern the fulfillment of end conditions. For the case of large deflections, the resultant equations from asymptotic analysis are presented. Their application to buckling under pure flexure shows various novel aspects. By a simple direct approach, investigation is pursued beyond the critical state: the buckled configuration turns out to be stable even for laxer constraints...
To define the asymptotic behaviour of elastic, one-dimensional structural elements, a vanishing parameter is introduced, associated with the small elongations of high strength materials. Two categories of non linear problems are recognized, concerning respectively "rods" and "beams" according as the slenderness has the order and . First approximation formulations are presented for either case and refinements prospected.
Formulations governing the free vibrations of shells are coordinated according to their foundations in the deduction from three-dimensional theory of elasticity by asymptotic procedures.
A compatible quadrilateral displacement field is translated along the coordinate lines on the midplane of the plate at intervals 1/3 the field width. Plate deflections are represented by a combination of such displacement fields. Energy variation equations furnish the equilibrium conditions. These equations, when written for the incomplete fields intersected by the contour, yield the boundary conditions.
A linearized formulation of the elastic theory of suspension bridges is confronted with early investigations in the field. For decades, the structure was schematized as a beam (deck or girder) relieved by a one parameter distribution of forces exerted by the cable, disregarding the influence of beam deflection on that distribution as given by the linearized approach. An anonymous note presented the essential conclusions of this theory anticipating results of investigations following the methods...
Download Results (CSV)