Search

Abstract: This paper presents a new finite-element formulation for the dynamic analysis of three-dimensional beams. The formulation is based on the geometrically exact three-dimensional beam theory in which the strain vectors are the only unknown functions of the arc-length parameter. The classical Newmark time integration scheme extended to the multiplicative group of spatial rotations is used and properly adapted for the strain-based formulation. The Generalized- method is used to enforce a numerical dissipation of higher modes. The update procedure needed in the iteration process is discussed in detail. The exact linearization of the governing equations is also presented. The performance of the formulation is demonstrated with numerical examples. [Copyright &y& Elsevier]

Abstract: Failure of concrete under compression results in a localized region of softened material subject to high strain. The paper attempts to find out the error of the numerical method for the mechanical analysis of planar reinforced-concrete beams subject to temperature increase simulating typical fire conditions at high temperatures, if the strain softening in concrete is considered, while employing continuous finite elements. The results are confronted with the formulation using constant-strain crack band elements in the localized regions combined with the continuous elements everywhere else. The width of the crack band is, in principle, temperature and stress–state dependent. In the paper we assume the crack band elements of constant width throughout the analysis, which may be a valid assumption at high temperatures, as indicated by some data given in literature. Results of the analyses of a two-story, two-bay reinforced concrete frame, designed strictly in accordance with the European standards, and subject to self weight, dead and service loads and, additionally, to the increasing fire-like thermal load are presented. The use of solely continuous finite elements, yet accounting for strain softening of material wherever it occurs, yields spatially oscillating results for strains around the localized region. This sometimes yields a totally false result or loss of convergence of the global Newton method. The width of the localized band tends to zero with the growing density of the finite-element mesh, with the results being highly mesh sensitive. The finite-element meshes where constant-strain crack band elements in the localized regions are combined with the continuous elements everywhere else yield, on the other hand, a computationally stable and accurate post-instability response for a wide range of crack-band element widths. Its critical point is, however, obtaining a reliable estimate of the width of the crack band element at high temperatures. This requires extensive experimental testing with hot concrete in compression. [Copyright &y& Elsevier]

Abstract: The paper presents a formulation of the geometrically exact three-dimensional beam theory where the shape functions of three-dimensional rotations are obtained from strains by the analytical solution of kinematic equations. In general it is very demanding to obtain rotations from known rotational strains. In the paper we limit our studies to the constant strain field along the element. The relation between the total three-dimensional rotations and the rotational strains is complicated even when a constant strain field is assumed. The analytical solution for the rotation matrix is for constant rotational strains expressed by the matrix exponential. Despite the analytical relationship between rotations and rotational strains, the governing equations of the beam are in general too demanding to be solved analytically. A finite-element strain-based formulation is presented in which numerical integration in governing equations and their variations is completely omitted and replaced by analytical integrals. Some interesting connections between quantities and non-linear expressions of the beam are revealed. These relations can also serve as useful guidelines in the development of new finite elements, especially in the choice of suitable shape functions. [Copyright &y& Elsevier]

Abstract: A new mathematical model for the non-linear analysis of two-layer planar beams considering flexible connections is introduced and an effective, strain-based finite element numerical solution method derived. The model and the solution method account for the exact geometrically non-linear behaviour in each separate layer. Material is assumed homogeneous but can be different in each layer. The shear strains are neglected. The laws of contact in both tangent and normal directions are taken non-linear. Numerical examples verify the proposed approach. The comparisons with numerical and experimental results from literature are made and the effects of uplift on ductility and stress distribution in beams are systematically explored. The theoretical model, combined with the present numerical formulation, has been found to result in realistic behaviour, while the numerical method proves to be accurate, reliable and computationally effective. [Copyright &y& Elsevier]

Abstract: The exact analytical solution of buckling in beams with multiple delaminations is presented. In order to investigate analytically the influence of axial and shear strains on buckling loads, the geometrically exact beam theory is employed with no simplification of the governing equations. The critical forces are then obtained by the linearized stability theory. The parametric studies are designed so that they give us fundamental understanding of the effects of the delamination number, length and position on the buckling load. The effect of shear is found to be of substantial importance. [Copyright &y& Elsevier]

A heuristic viscosity-type dissipation of strains is applied for controlling high frequency oscillation damping in a one-step time integration. The basic idea of the approach is to apply damping in locations, where it is needed, at times when it is needed. To this end a computationally efficient algorithm for identifying the need for damping is developed. The identification algorithm keeps track of the number of recent changes of signs of strain increments, which helps in decision whether damping should be engaged or not. A special scaling function is introduced to smoothen the transition between the damped and undamped phases. The approach is verified in the analysis of the geometrically exact plane elastic beam. [ABSTRACT FROM AUTHOR]

A family of new beam finite elements for geometrically and materially non-linear static analysis of reinforced concrete planar frames is derived, in which strain measures are the only interpolated unknowns, and where the constitutive and equilibrium internal forces are equal at integration points. The strain-localization caused by the strain-softening at cross-sections is resolved by the introduction of a `short constant-strain element''. Comparisons between numerical and experimental results on planar frames in pre- and post-critical states show both good accuracy and computational efficiency of the present formulation. [Copyright &y& Elsevier]

Abstract: A new finite element formulation is presented for the non-linear analysis of two-layer composite planar frames with an interlayer slip. For each layer the geometrically non-linear Reissner’s beam theory is assumed. A small slip between the layers is considered. Non-linear, time-dependent constitutive models for the layers, and a non-linear relationship between the slip and the shear stress at the interface are accounted for. As only a few finite elements are needed to describe a beam or column of a frame with great precision, the new finite element formulation is prefectly suited for practical calculations. [Copyright &y& Elsevier]

This paper presents a new finite element formulation of the ‘geometrically exact finite-strain beam theory’. The governing equations of the beam element are derived in which the strain vectors are the only unknown functions. The consistency condition that the equilibrium and the constitutive internal force and moment vectors are equal, is enforced to be satisfied at chosen points. The solution is found by a collocation algorithm. The linearity of the strain space not only simplifies the application of Newton’s method on the non-linear configuration space, but also leads to the strain-objectivity of the proposed method. The accuracy and the efficiency of the derived numerical algorithm are demonstrated by several examples. [Copyright &y& Elsevier]

An energy conserving finite-element formulation for the dynamic analysis of geometrically non-linear beam-like structures undergoing large overall motions has been developed. The formulation uses classical displacement-based planar beam finite elements described in an inertial frame. It takes into account finite axial, bending and shear strains. A theoretically consistent approach is used to derive a novel and simple energy conserving scheme, using the unconventional incremental strain update rather than the standard strong form. Numerical examples demonstrate perfect energy and momenta conservation, stability and robustness of the scheme, and good convergence properties in terms of both the Newton–Raphson method and time step size. [Copyright &y& Elsevier]