Flexural-Torsional Buckling of Cantilever Strip Beam-Columns with Linearly Varying Depth

Abstract

International audienceIn this paper, one investigates the elastic flexural-torsional buckling of linearly tapered cantilever strip beam-columns acted by axial and transversal point loads applied at the tip. For prismatic and wedge-shaped members, the governing differential equation is integrated in closed form by means of confluent hypergeometric functions. For general tapered members (0 <(h(max)-h(min))/h(max)< 1), the solution to the boundary value problem is obtained in the form of a Frobenius' series, which is shown to converge in the interior of the domain and at the boundary if and only if 0 <(h(max)-h(min))/h(max)< 1/2. Therefore, for 1/2 <=(h(max)-h(min))/h(max)< 1 the Frobenius' series solution cannot be used to establish the characteristic equation for the cantilever beam-columns; the problem is then solved numerically by means of a collocation procedure. Some of the analytical solutions (buckling loads) were compared with the results of shell finite-element analyses and an excellent agreement was found in all cases, thus validating the mathematical model and confirming the correctness of the analytical results. The paper closes with a discussion on the convexity of the stability domain (in the load parameter space) and the accuracy of approximations based on Dunkerley-type theorems

Development of analytical vibration solutions for microstructured beam model to calibrate length scale coefficient in nonlocal Timoshenko beams

“…The hypergeometric function has earlier been adopted to solve the transverse vibration problem of non-uniform annular plates (Duan et al, 2005), the lateral-torsional buckling problem of linearly tapered cantilever (Challamel et al, 2007), the axisymmetric bending problem of micro/nanoscale circular plates , the buckling problem of columns with allowance for self-weight (Duan and Wang, 2008), and axisymmetric transverse vibration problem of circular cylindrical shells with variable thickness (Duan and Koh, 2008), the flexural-torsional buckling problem of cantilever (Challamel et al, 2010), and the lateral-torsional stability boundaries for polygonally depthtapered strip cantilevers (Andrade et al, 2012). The Frobenius companion matrix of a second kind Chebyshev polynomial U nÀ1 ðx=2Þ is given by (Horn and Johnson, 1990) …”

Deflection of a Partially Composite Beam Considering the Effect of Shear Deformation

“…On the other hand, the tensile mode induces unstable fracture with limits of energy absorption [22,23]. Therefore, the strength of the compound can be determined by optimizing the interface properties between the reinforcing fibers and the matrix phase [24,25]. The two beams forming PCB are interconnected by a very thin adhesive with a high performance (good cohesion, mechanical strength and thermal).…”

Lateral-Torsional Stability Boundaries for Polygonally Depth-Tapered Strip Cantilevers Under Multi-Parameter Point Load Systems—An Analytical Approach

“…Therefore, the general solutions of Eqs. (24) and (25) [22][23][24][25][26] for previous applications in structural mechanics. The theory of confluent hypergeoihetric functions is discussed at great length and detail in the monographs by Buchholz [19], Slater [21] and Tricomi [18]; a useful summary of facts and relations is given in Ref.…”