Two-node Beam Element Research Articles

3D Analyses of Buildings under Vertical Component of Earthquakes

This study first investigates how to perform the 3D dynamic analysis of buildings under the vertical component of earthquakes. The analysis results indicate that (1) dividing a main girder into two elements is required to perform the vertical earthquake analysis; (2) including secondary beams for the building analysis is similar to refine modeling of the building (at this time, one building member, such as a secondary beam or a portion of the main girder, modeled by a two-node beam element can also produce an accurate result); (3) neglecting the floor stiffness in the vertical direction is suitable, if the floor thickness is not too thick; and (4) the required vertical effective mass ratio is suggested to be 80%. In the second part of this paper, 1,080 time-history analyses and 180 static analyses of reinforced concrete buildings were performed in order to investigate the relationships of extreme column axial forces and beam moments between vertical earthquake and dead loads. The analysis results indicate...

Finite rotation quadrilateral element for multi-layer beams

The paper presents the finite rotations beam equations derived on use of the generalized Reissner hypothesis with a scalar parameter for the transverse extension. The beam strain and change of curvature measures are obtained from the right stretch strain, and the virtual work is given for Biot-type stress and couple resultants. The strain energy for the first-order isotropic elastic material is assumed in terms of the right stretch strain, and constitutive equations for the beam stress and couple resultants are derived. Two finite rotation elements are developed from the derived beam equations: a beam element with the transverse stretch and a quadrilateral element. First, the beam element with the uniformly under-integrated tangent operator is developed. Next, the formula linking the middle-line variables and the interface variables of the beam is introduced consistently with the generalized Reissner kinematics. Linearization of this formula is performed, and the derived tangent operator is used to convert the two-node beam element to a four-node quadrilateral. Both the finite elements have been tested on several numerical examples, some of highly non-linear characteristics, and their accuracy is very good. It has been established that the quadrilateral element, which is intended for applications to multi-layer beams, performs very well for high elemental aspect ratios, and can therefore be applied to modelling of very thin layers. Copyright © 1999 John Wiley & Sons, Ltd.

Finite element model with continuous transverse shear stress for composite laminates in cylindrical bending

In the double superposition hypothesis, the global inplane displacement, which applies to the whole laminate, is enriched by local displacements which are restricted to each individual ply. To avoid the number of d.o.f.s growing with the number of plies, the transverse shear stress continuity is enforced as usual whereas the inplane displacement continuity is “doubly” constrained for two different groups of the local displacement. Based on the hypothesis, a two-node beam element is attempted. The element has the deflection and its derivative as its nodal d.o.f.s. Despite the fact that interpolated deflection is a cubic function of the longitudinal coordinate, the element yields poor accuracy. The cause is sorted out to be an algebraic constraint in the transverse shear. To overcome the constraint, a heterosis node is added. Remarkable improvement of the element accuracy is noted.

Geometric non-linear analysis of three-dimensional guyed towers

Three-dimensional geometric non-linear analysis of guyed towers using linear isoparametric formulation within an updated Lagrangian coordinate framework is presented. The complex non-linear behaviour of the guy cables is simplified by the equivalent modulus approach. Shear locking of the two-noded beam element is corrected by reduced order of integration and altering the elastic coefficient for the transverse shear. The formulation is general enough to include transverse shear effects, eccentricity of the centroidal axes from the beam shear centre and the product of inertia of the beam cross-section. A typical guyed tower example is solved and results are compared with the published work.

Moving finite element analysis for the elastic beams in contact problems

The contact problem of a linear elastic beam with a rigid barrier is considered, in which the contact surface is assumed to be frictionless. The problem contains the characteristic of moving boundaries as the contact regions expand or reduce in size when the external loads alter. Starting from the variational principles, we derived the interface equations as well as the governing equation. In addition to matching the deflections and the slopes with the rigid barrier at the marginal nodes of the contact regions, the interface equations also have to be satisfied there. In essence, the interface equations are designed to locate the unknown and moving marginal nodes. Although it is confined within the framework of small deformation and linear elastic material behavior, the problem exhibits high nonlinearity due to the moving nature of the marginal nodes. In this paper, we present a moving finite element analysis employing incremental procedures and an iterative numerical scheme to tackle the problem. A fixed number of two-node beam elements are used in the moving finite element analysis and the size of the elements varies as the loads alter. A couple of examples, whose exact solutions are obtainable, are chosen to demonstrate the accuracy and efficiency of the proposed numerical algorithm.

Hybrid-Stress Reduced Mindlin Isoparametric Elements for the Analysis of Thin Plates

ABSTRACT Hybrid-stress isoparametric finite elements are developed for the analysis of thin plates utilizing independent interpolations for transverse displacement and cross-section rotations. The formulation is based on earlier hybrid-stress plate elements that utilize Mindlin-type displacement fields and include transverse shear stress and transverse normal stress contributions. By neglecting the contributions of transverse shear and normal stresses to the complementary strain energy, isoparametric thin plate elements are obtained that have the same performance characteristics as the non-reduced element in the thin plate limit. This is illustrated for a two-node beam element. In addition to the ease of formulating isoparametric thin plate elements using C ° displacement interpolations, the primary advantage of this approach over the nonreduced element is the significant savings of computation time for element stiffness generation that is made possible. Computational considerations are illustrated for an 8-node invariant isoparametric plate element.