Mahjoub El Nimeiri

Bio: Mahjoub El Nimeiri is an academic researcher from Northwestern University. The author has contributed to research in topics: Stiffness matrix & Beam (structure). The author has an hindex of 3, co-authored 3 publications receiving 134 citations.

Large-Deflection Spatial Buckling of Thin-Walled Beams and Frames

Abstract: The potential energy expression and the (14 by 14) stiffness matrix of a straight thin-walled beam element of open asymmetric cross section, subjected to initial axial force, initial bending moments, and initial bimoment, are derived. The transformation matrix relating the forces and displacements (including bimoment and warping parameter) at the adjacent end cross section of two elements meeting at an angle is deduced as the limiting case of a transfer matrix of a curved beam. To cope with asymmetric cross sections, some element displacements and forces are referred to the shear center and others to the cross-sectional centroid and the matrix for transformation from shear center to centroid is set up. The incremental larger-displacement analysis is formulated using the Eulerian coordinate approach with updating of the local coordinate systems at each load increment. The deformed beams are imagined to be composed of straight elements. Results of lateral post-buckling analysis of various beams are presented.

Stiffness Method for Curved Box Girders at Initial Stress

Abstract: A method of analysis of the global behavior of long curved or straight single-cell girders with or without initial stress is presented. It is based on thin-wall beam elements that include the modes of longitudinal warping and of transverse distortion of cross section. Deformations due to shear forces and transverse bimoment are included, and it is found that the well-known spurious shear stiffness in very slender beams is eliminated by virtue of the fact that the interpolation polynomials for transverse displacements and for longitudinal displacements (due to rotations and warping) are linear and quadratic, respectively, and an interior mode is used. The element is treated as a mapped image of one parent unit element and the stiffness matrix is in integration in three dimensions, which is numerical in general, but could be carried out explicitly in special cases. Numerical examples of deformation of horizontally curved bridge girders, and of lateral buckling of box arches, as well as straight girders, validate the formulation and indicate good agreement with solutions by other methods.

Finite Element for Buckling of Curved Beams and Shells with Shear

Abstract: Inclusion of shear deformations allows the bending theory to be extended to relatively thick beams and shells and, at the same time, simplifies the finite element formulation for both thick and thin beams because monotonic convergence may be achieved without ensuring continuity of displacement derivatives between adjacent elements. Consequently, on may use low order interpolation polynomials, including linear ones. This is particularly useful in the case of curved beams because with higher order interpolation polynomials it is very difficult to satisfy exactly the conditions of no self-staining at rigid body rotations and of availability of all constant strain states, while with linear displacement interpolation polynomials and a straight shape of the element these requirements are easily met.

Large displacement analysis of three‐dimensional beam structures

Abstract: An updated Lagrangian and a total Lagrangian formulation of a three-dimensional beam element are presented for large displacement and large rotation analysis. It is shown that the two formulations yield identical element stiffness matrices and nodal point force vectors, and that the updated Lagragian formulation is computationally more effective. This formulation has been implemented and the resulted of some sample analyses are given.

Stiffness Matrix for Geometric Nonlinear Analysis

Abstract: A new stiffness matrix for the analysis of thin walled beams is derived. Starting from the principle of virtual displacements, an updated Lagrangian procedure for nonlinear analysis is developed. Inclusion of nonuniform torsion is accomplished through adoption of the principle of sectorial areas for cross‐sectional displacements. This requires incorporation of a warping degree of freedom in addition to the conventional six degrees of freedom at each end of the element. Problems encountered in the use of this and similar matrices in three‐dimensional analysis are described.

Lateral–Torsional Buckling of Singly Symmetric Tapered Beams: Theory and Applications

Abstract: A general variational formulation to analyze the elastic lateral-torsional buckling (LTB) behavior of singly symmetric thin-walled tapered beams is presented, numerically implemented, validated and illustrated. It (1) begins with a precise geometrical definition of a tapered beam; (2) extends the kinematical assumptions traditionally adopted to study the LTB of prismatic beams; (3) includes a careful derivation of the beam total potential energy; and (4) employs Trefftz's criterion to ensure the beam adjacent equilibrium. In order to validate and illustrate the application and capabilities of the proposed formulation, several numerical results are presented, discussed and, when possible, also compared with values reported by other authors. These results (1) are obtained by means of the Rayleigh-Ritz method, using trigonometric functions to approximate the beam critical buckling mode, and (2) concern the critical moments of doubly and singly symmetric web-tapered I-section simply supported beams and cantilevers acted by point loads. In particular, one shows that modeling a tapered beam as an assembly of prismatic beam segments is conceptually inconsistent and may lead to rather inaccurate (safe or unsafe) results. Finally, it is worth mentioning that the paper includes a state-of-the-art review concerning one-dimensional analytical formulations for the LTB behavior of tapered beams.