Numerical study of a steel sub-frame in fire

Steel-framed buildings are generally designed with “simple” shear-resisting connections, and lateral forces are resisted by vertical bracing and shear walls. When a beam is considered then the effects of the longitudinal restraints by the adjacent structure and the rotational restraint by the connections has to be taken into account. Because of structural interaction, the beam behaviour at elevated temperature is rather complex.This paper presents a numerical parametric study of a structural system consisting of an exposed steel beam restrained between a pair of fire protected steel columns. The structural sub-frame is modelled using 3D shell elements, thereby taking into account the effect of the local failure modes, and the realistic behaviour of the sub-frame exposed to natural fire. The numerical model accounts for the initial geometrical imperfections, nonlinear temperature gradient over the cross-section, geometrical and material nonlinearity and temperature dependent material properties.Results obtained using a general Finite Element software – LUSAS and a fire dedicated software – SAFIR, are compared. The influence of following variables: beam span/depth ratio, lateral restraint, gradient temperature within the cross-section and mechanical load level is presented in the paper. The failure modes, the development of the internal forces and displacements throughout the analysis are considered to exemplify the effects of the variables considered.     

Optimization of inelastic cylindrical shells with internal supports

A non-linear programming method is developed for optimization of inelastic cylindrical shells with internal ring supports. The shells under consideration are subjected to internal pressure loading and axial tension. The material of shells is a composite which is considered as an anisotropic inelastic material obeying the yield condition suggested by Lance and Robinson. Taking geometrical non/linearity of the structure into account optimal locations of internal ring supports are determined so that the cost function attains its minimum value. A particular problem of minimization of the mean deflection of the shell with weakened singular cross sections is treated in a greater detail.     

Numerical modeling of softening hinges in thin Euler–Bernoulli beams

This paper presents new finite elements for thin Euler–Bernoulli beams that incorporate the softening hinges observed at failure. The proposed methods rely crucially on the identification of the classical notion of inelastic hinge with strong discontinuities of the generalized displacements describing the beam’s deformation. The development of a multi-scale framework that effectively incorporates the localized dissipative mechanisms associated with these discontinuous solutions into the large-scale problem of the beam, or general frame system, defines a crucial step undertaken here. This framework defines the setting of its numerical implementation by finite elements enhanced with the singular strains corresponding to the discontinuities. A general procedure is presented that leads, in particular, to finite elements free of stress-locking and that resolve exactly the kinematics of the hinge. Several numerical simulations are presented to illustrate the performance of the proposed methods.     

Two-dimensional modeling of material failure in reinforced concrete by means of a continuum strong discontinuity approach

The paper presents a new methodology to model material failure, in two-dimensional reinforced concrete members, using the Continuum Strong Discontinuity Approach (CSDA). The mixture theory is used as the methodological approach to model reinforced concrete as a composite material, constituted by a plain concrete matrix reinforced with two embedded orthogonal long fiber bundles (rebars). Matrix failure is modeled on the basis of a continuum damage model, equipped with strain softening, whereas the rebars effects are modeled by means of phenomenological constitutive models devised to reproduce the axial non-linear behavior, as well as the bond-slip and dowel effects. The proposed methodology extends the fundamental ingredients of the standard Strong Discontinuity Approach, and the embedded discontinuity finite element formulations, in homogeneous materials, to matrix/fiber composite materials, as reinforced concrete. The specific aspects of the material failure modeling for those composites are also addressed. A number of available experimental tests are reproduced in order to illustrate the feasibility of the proposed methodology.     

Thin element applications of a new formulation for C structural elements

A new formulation was proposed recently for the removal of the shear and membrane locking mechanisms from the finite element equations of the structural C⁰ shell, plate and beam elements. The use of full integration with the proposed formulation does not allow development of the zero energy modes or the softening effects, usually associated with the use of the technique of reduced integration in C⁰ plate and shell element applications. In the present paper a beneficial side effect of the new formulation is presented with regard to the development of the purely machine dependent locking. Questions concerning the introduction of softening effects by the new formulation in some flat C⁰ plate/shell element applications are addressed.     

Microstructure based two-scale modelling of soft tissues

A technique suitable for the modelling of large deforming biological tissues with a nearly periodic microstructure is presented in this work. The proposed approach takes into account the heterogeneous material constitution and geometrical arrangement of the tissues at the microstructural level. The global material properties are described in terms of the homogenized (effective) parameters. Numerical simulations are focused on the mechanical behaviour of an arterial wall.     

The application of the thin-walled box beam element to multibox bridge analysis

An application of the recently developed thin-walled box beam element to the analysis of multibox bridges which arises in practical design, is presented. The thin-walled box beam element, which also takes account of warping distortional effects, when combined with traditional beam elements into a grillage model may adequately represent the three-dimensional behaviour of multibox superstructure. Equivalent sectional properties for the transverse grillage members across individual boxes are computed from a frame analysis. A numerical iterative procedure is introduced to take account of the interaction due to distortion.Comparisons with other numerical methods and model experiments demonstrate the accuracy and economy of the proposed method.     

Numerical and analytical investigation of collapse loads of laced built-up columns

Built-up columns are often used in steel buildings and bridges providing economical solutions in cases of large spans and/or heavy loads. Two main effects should be taken into account in their design that differentiate them from other structural members. One is the significant influence of shear deformations due to their reduced shear rigidity. The second is the interaction between global and local buckling. These effects are addressed here from both a numerical and an analytical point of view for laced built-up columns. It is concluded that the largest loss of capacity occurs when the local and global Euler critical stresses and the yield stress all coincide. This reduction in capacity becomes more prominent in the presence of imperfections, reaching magnitudes in the order of 50%. Despite the detrimental effects of mode interaction many major design codes do not provide sufficient pertinent guidance. In order to address this issue, a simple analytical method is proposed for calculating the collapse load of laced built-up members taking into account the above effects as well as global imperfections, local out-of straightness and plasticity, which is then verified by means of nonlinear finite element analysis, using either beam or shell elements. The proposed method is found to provide improved accuracy in comparison to EC3 specifications in cases of global elastic failure.     

Nonlinear flexural oscillations of orthotropic shallow spherical shells

The effect of curvature and polar orthotropy on nonlinear dynamic behaviour of a shallow spherical shell is investigated in the present paper. Numerical solutions based on an assumed two-term modeshape for the axisymmetric, forced (uniform pressure) and free vibrations are obtained for different shell geometries and orthotropic material constants. The results, when specialised for the case of isotropic material, are in good agreement with those available in the literature. Based on a one-term modeshape solution, the values of the geometric parameter at which the transition from hardening to softening type of nonlinearity takes place and where the reversal of the softening trend occurs are obtained for different values of the orthotropic constants.     

Reduced basis technique for evaluating the sensitivity of the nonlinear vibrational response of composite plates

A reduced basis technique and a computational procedure are presented for generating the nonlinear vibrational response, and evaluating the first-order sensitivity coefficients of composite plates (derivatives of the nonlinear frequency with respect to material and geometric parameters of the plate). The analytical formulation is based on a form of the geometrically nonlinear shallow shell theory with the effects of transverse shear deformation, rotatory inertia and anisotropic material behavior included. The plate is discretized by using mixed finite element models with the fundamental unknowns consisting of both the nodal displacements and the stress-resultant parameters of the plate. The computational procedure can be conveniently divided into three distinct steps. The first step involves the generation of various-order perturbation vectors, and their derivatives with respect to the material and lamination parameters of the plate, using Linstedt-Poincaré perturbation technique. The second step consists of using the perturbation vectors as basis vectors, computing the amplitudes of these vectors and the nonlinear frequency of vibration, via a direct variational procedure. The third step consists of using the perturbation vectors, and their derivatives, as basis vectors and computing the sensitivity coefficients of the nonlinear frequency via a second application of the direct variational procedure. The effectiveness of the proposed technique is demonstrated by means of numerical examples of composite plates.     

Nonlinear primary resonance of imperfect spiral stiffened functionally graded cylindrical shells surrounded by damping and nonlinear elastic foundation

In this paper, an analytical method is used to study the nonlinear primary resonance of imperfect spiral stiffened functionally graded (SSFG) cylindrical shells with internal stiffeners. The SSFG cylindrical shell is surrounded by linear and nonlinear elastic foundation and the effect of structural damping on the system response is also considered. The material properties of the shell and stiffeners are assumed to be continuously graded in the thickness direction. Three-parameter nonlinear elastic foundation model is consists of two-parameter linear elastic foundation (Winkler and Pasternak) and one hardening/softening cubic nonlinearity parameter. Based on the von Kármán nonlinear equations and the classical plate theory of shells, the strain–displacement relations are derived. The smeared stiffener technique is used to the model of the internal stiffeners. Using the Galerkin method, the partial differential equations of motion are discretized. The nonlinear primary resonance is analyzed by means of the multiple scales method. The effects of various geometrical characteristics, material parameters and elastic foundation coefficients are investigated on the nonlinear primary resonance.

     

A Phenomenological Discrete Brittle Damage-Mechanics Model for Fatigue of MEMS Devices With Application to LIGA Ni

Fatigue initiation and failure of various microelectromechanical systems (MEMS) is of significant importance as they gain widespread acceptance in sensors and electronics. This paper presents an approach for utilizing available experimental fatigue data to evaluate the fatigue lives of MEMS components. The approach is based on a phenomenological discrete material representation in which a domain is represented by a collection of rigid elements that interacts via springs along their boundaries. The principles of continuum damage mechanics are used to degrade the spring stiffnesses as brittle damage occurs when the domain is subjected to fatigue loading. The model utilizes experimental stress–life data for LIGA Ni to identify the material properties used in the model. The proposed model captures the statistical distribution of material properties and geometrical randomness of the microstructure commonly observed in a wide variety of MEMS. Consequently, simulations that account for the variability in fatigue life can be readily performed. The model is applied to a dog-bone-shaped specimen to evaluate the influence of material heterogeneity and material flaws on fatigue crack initiation life and scatter. The ability of the model to predict the fatigue life of different types of MEMS devices and loading conditions is also demonstrated by simulating the fatigue stress–life behavior of a MEMS resonator support beam. $hfill$[2008-0087]      

Two-dimensional finite element upper bound limit analysis of masonry bridges

A two-dimensional model for the evaluation of the load carrying capacity of masonry bridges is proposed that takes into account the strengthening effects due to arch–fill interaction observed in experimental tests. Upper bounds on the collapse load and the corresponding mechanism are obtained by means of a finite element application of the Kinematic Theorem of Limit Analysis. Arches and piers are modelled as beams made up of non-tensile resistant (NTR) and ductile in compression masonry, while the fill is represented as a cohesive-frictional material with tension cut-off. Kinematically admissible mechanisms are obtained by discretizing the fill domain with triangular elements and including velocity discontinuities in order to increase the degrees of freedom of the model and thus reduce locking; arches and piers are discretized by two-node straight beam elements. A piecewise linearization of the limit domains allows the upper bound on the collapse load and the corresponding mechanism to be obtained as a solution of a Linear Programming problem. The capabilities and the validity limits of the proposed numerical model are shown in two examples. The collapse test on a real single span bridge is simulated and discussed in the first example; a multi-span bridge is analysed in the second, where complex interactions between arches, piers and fill are obtained.     

Large displacements of shells including material nonlinearities

The paper presents a finite element formulation of shells with large deflections including elastoplastic material behaviour. The elements utilized are the so-called degenerated shell elements, with special emphasis on the simple 4 node quadrilateral. Both the total Lagrangian and the updated Lagrangian formulation are considered. For the treatment of plastic behaviour the concept of a layered element model is proposed and investigated for both the tangential modulus method and the initial load method. In the final section sample problems are presented and compared with reference solutions. It is shown that the 4 node element is very well-suited to the class of problems under consideration. It is characterized by an easy applicability, high accuracy and low rates of computer time.In Appendix A an analytical solution of a cantilever beam, subjected to an end load, including geometrical and material nonlinearities is presented.     

A new analytical model for switching time of a perforated MEMS switch

In this paper, the design of a low-k meander based MEMS shunt capacitive switch with perforated beam meander has been presented. A closed form analytical model to calculate the switching time of designed structure is proposed. The model is based on modified Mejis and Fokkema’s capacitance model and linearization of non-linear electrostatic force on the switch beam. The model is utilized in evaluating the switching time for uniform as well as non-uniform serpentine meander designs, considering different values of actuation voltage and a wide variation of switching parameters. This work takes into account the beam perforation, fringing field and stiffness effect simultaneously altogether. The results obtained for both the meander designs under every design specifications has been found out to be less than or approximately equal to 100 µs. These model based results are then compared with 3D FEM simulated values. Comparative Analysis indicated that the model results and simulation results are in close agreement with each other.

     

A thin-walled box beam finite element for curved bridge analysis

Practical design of single and multispan curved bridges requires an analysis procedure which is easy and economical to use, and provides a physical insight into structural response under general loading conditions. In the work presented, the thin-walled beam theory has been directly combined with the finite element technique to provide a new thin-walled box beam element. The beam element includes three extra degrees-of-freedom over the normal six degrees-of-freedom beam formulation, to take into account the warping and distortional effects as well as shear. The beam may be curved in space and variable cross-sections may be included. The performance of the box beam element has been compared favourably against results obtained from full 3D shell element analysis, differential equation solutions and experimental results.     

Domain decomposition techniques for the efficient modeling of brittle heterogeneous materials

This paper describes a computational tool for the efficient study of failure in brittle heterogeneous materials. By means of several examples, it is demonstrated that the proposed tool is adequate for the analysis of materials that show localized failure modes. This case is particular since the main non-linearities concentrate in a small area compared to the whole specimen. The use of the method is preferred when the mesoscopic structure plays a crucial role during failure processes and needs to be fully taken into account in order to accurately tackle damage growth and propagation in the material. The present strategy is based on a Domain decomposition technique. Its performance is improved by selectively processing inelastic regions and reducing the number of operations in the remaining elastic areas. A four point bending test and the fracturing of a heterogeneous concrete specimen are presented as illustrations. They demonstrate that computational costs can be significantly reduced when the proposed strategy is applied to damage analysis.