Non-linear finite element dynamic analysis of two-dimensional concrete structures

This paper presents a numerical procedure for predicting the non-linear dynamic response of plane and axisymmetric reinforced concrete structures. Isoparametric elements with special embedded axial members are used to discretize concrete and steel in space. A summary of a rate and history dependent constitutive model for progressive failure analysis of concrete is given in which the compression behaviour is modelled as a strain rate sensitive elasto-viscoplastic material and in tension as strain rate dependent linear elastic strain softening material. The different rales governing the pre-failure and post-failure behaviour in compression and tension are developed in which the strain rate dependency is included. Steel is modelled as a strain rate dependent uniaxial elasto-viscoplastic material. Explicit central difference scheme in conjunction with an energy balance check is employed for time integration of equations of motion. A computer program for linear and non-linear dynamic analysis of concrete structures is described. Finally, some numerical applications are presented.     

Nonlinear finite element analysis of concrete structures using new constitutive models

Nonlinear finite element analysis was applied to various types of reinforced concrete structures using a new set of constitutive models established in the fixed-angle softened-truss model (FA-STM). A computer code FEAPRC was developed specifically for application to reinforced concrete structures by modifying the general-purpose program FEAP. FEAPRC can take care of the four important characteristics of cracked reinforced concrete: (1) the softening effect of concrete in compression, (2) the tension-stiffening effect by concrete in tension, (3) the average (or smeared) stress–strain curve of steel bars embedded in concrete, and (4) the new, rational shear modulus of concrete. The predictions made by FEAPRC are in good agreement with the experimental results of beams, panels, and framed shear walls.     

A hybrid,finite element—finite difference approach to simplified large deflection analysis of structures

A new and considerably simplified solution technique for geometrically nonlinear problems is introduced. In contrast to the existing numerical methods, the present approach obtains an approximate large deflection pattern from the linear displacement vector by successively employing updated correction factors. Conservation of energy principle yields a general expression for these subsequent corrections. While the linear portion of the strain energy can be computed using finite element approach, evaluations of its nonlinear counterparts often require mathematical discretization techniques. The simple, self-correcting iterative procedure is unconditionally stable and its fast oscillatory convergence offers further computational efficiency. To illustrate the application of the proposed method and to assess its accuracy, moderately large deflections of beam, plate and flexible cable structures have been computed and compared with known analytical solutions. If required, the obtained results—which are acceptable for most design purposes—can be further improved.     

A three-dimensional finite element program to predict ultimate fracture failure load

A finite element computer program using an eight-noded three-dimensional isoparametric finite element is developed to predict the initiation and propagation of fracture, load-displacement history and failure load in elastoplastic structural systems subjected to monotonically increasing loads. Isotropie material is considered. The program is based on small deformation theory and uses an incremental loading technique to load the structure. The approach uses two types of piecewise linear approximations for the non-linear portion of the actual uniaxial stress-strain curve for the material: (i) the tangent modulus concept and (ii) the secant modulus concept. Either the St. Venant or von Mises yielding criteria can be used to predict yielding or fracture. Three different methods of calculating element principal stresses/strains are incorporated to apply the yield criterion. The energy at fracture is redistributed by using the ‘zero modulus unload-reload scheme’. Two different problems are solved using the developed program to demonstrate its capabilities and accuracy: (i) a center cracked panel and (ii) a tubular T-connection. The results obtained by the finite element analyses compare well with the available results from experimental tests on similar specimens.     

Mesh, gravity and load effects on finite element simulations of blast loaded reinforced concrete structures

The behavior and design of reinforced concrete blast resistant structures are supported by intensive numerical simulations, and the effects of various parameters on the results is of great interest. Finite element simulations were performed in the nonlinear dynamic domain with modified concrete and steel constitutive models. Ten different cases were implemented, each with different reinforcement details. In addition, each case included both a coarse mesh and a fine mesh to determine the effects of mesh resolution on the numerical simulations. Gravity and loading conditions were altered to investigate their influences on the results. Deformations and stress distributions in both the concrete and steel were examined to determine the composite structural behavior and the extent of predicted damage for the various cases. The observations from these analyses highlighted relationships between the simulation parameters and the corresponding outcome. Conclusions and recommendations are presented that could assist in the development of efficient numerical simulations in this general area.     

Application of a new stress finite element to analysis of shell structures

A new stress finite element for analysis of shell structures of arbitrary geometry and loading has been introduced in Ref. [1]. The purpose of the present paper is to demonstrate the versatility of the proposed element with respect to all kinds of shell structures.     

Evaluation of a finite element modelling approach for welded aluminium structures

Experimental and numerical studies were carried out to investigate the behaviour of quasi-statically loaded fillet-welded connections in aluminium alloy EN AW 6082. The components were designed so that fracture should occur in the heat-affected-zone (HAZ), which was also the case in the experiments. In the numerical study, the components were modelled in LS-DYNA using shell elements. A user-defined material model comprising the Barlat and Lian anisotropic yield criterion and a ductile fracture criterion was adopted. The strength and hardening data for the HAZ, weld and base material were taken from existing experimental data in the literature. The constants for the yield criterion were identified from uniaxial tensile tests by various methods, and the set of constants that best represents the measurements was adopted in the numerical analysis. Reasonable estimates on ductility were obtained by the simulations when a refined mesh was used, while the strength was somewhat over-predicted.     

Dynamic finite element analysis of nonaxisymmetric structures

A dynamic finite element method of analysis is developed for structural configurations which are derived from axisymmetric geometries but contain definite nonaxisymmetric features in the circumferential direction. The purpose of the analysis is to develop a method which will take into consideration the fact that the stress and strain conditions in these geometries will be related to the corresponding axisymmetrie solution. This analysis is an extension of previously published work in which a similar approach was developed for static structural problems. The analysis is developed in terms of a cylindrical coordinate system r, θ and z. As the first step of the analysis, the geometry is divided into several segments in the r-θ plane. Each segment is then divided into a set of quadrilateral elements in the r-z plane. The axisymmetric displacements are obtained for each segment by solving a related axisymmetric configuration. A perturbation analysis is then performed to match the solutions at certain points between the segments, and obtain the perturbation displacements for the total structure. The total displacement is then the axisymmetric displacement plus the perturbation displacement. The analysis allows for elastic-plastic materials with orthotropic yield criterion based on Hill's yield function and kinematic strain hardening. The finite element dynamic equations are solved by finite differences by dividing the time domain into incremental steps. The solution has been programmed on a computer and applied to a number of examples.     

An elastic-plastic finite element analysis of a CT fracture specimen

Two- and three-dimensional finite element calculations are presented for a 1TCT-specimen. The constitutive equations of the material are based upon the v. Mises yield criterion with isotropic hardening considering different hardening moduli. The results are compared with other finite element calculations and with experimental data. The agreement is quite good. It is confirmed that the state of stress in a 1TCT-specimen tends more to plane stress than to plane strain behaviour. Recommendations for the application of ADINA to this class of problems are given.     

Constitutive modeling of concrete in finite element analysis

Approaches generally used in defining constitutive relations for concrete are reviewed. A computer program developed for the three-dimensional finite element analysis of complex reinforced, prestressed, and refractory concrete systems is described. The constitutive models based on isotropic elastic, orthotropic elastic, and plasticity formulations, which are implemented in that program, are discussed in detail. The program incorporates nonlinear material properties, cracking in concrete, shear transfer in cracked reinforced concrete sections, and time dependent effects such as creep, shrinkage, and transient temperature distributions. A wide range of structural problems are analyzed to demonstrate the applicability of the computer program. Comparisons between predictions with different constitutive models, and between predictions and test results are made.     

Nonlinear viscoelastic stress analysis—a finite element approach

This paper describes a finite element algorithm developed for analysis of nonlinear viscoelastic materials. A single integral constitutive law proposed by Schapery is used to describe viscoelastic material behavior. Work leading to this paper focused on adhesives, but the FE formulation is general and readily extended to structural systems other than plane strain, plane stress and axisymmetric analysis as described. Cartesian strain components are written in terms of current and past stress states. Thus strains are conveniently defined by a stress operator that includes instantaneous compliance and hereditary strain which is updated by recursive computation. Equilibrium at each time step is insured with a modified Newton Raphson technique, incorporating convergence acceleration. Verification analyses show excellent agreement with experimental data for FM-73 adhesive systems. A plane strain analysis of a butt joint is included.     

Non-linear analysis of structures by the finite element method as a supplement to a linear analysis

The discrete elements of finite dimensions which replace the structural continuum in the finite element method can always be chosen sufficiently small that the linear relations between element deformations and element stresses remain valid to the same degree of approximation as is considered acceptable in the linear theory of elasticity. This observation formed the basis for the treatment of geometrical nonlinearities by Argyris and his co-workers in their natural mode technique [1]and [2].Here we give an alternative development of the theory. The element deformations, linearly related to nodal displacements and rotations in a local coordinate system, are expressed as analytic functions of the nodal coordinates in the global system. Then, for structures with an initially linear behaviour, the stability and postbuckling analysis is developed on the basis of the general theory founded by Koiter [3].The theory is illustrated by the example of frame-structures. The location of the nodal points is defined in terms of the displacement vector, while the orientation of an orthogonal triad attached to each nodal point is described by means of modified angular coordinates of Euler. The accuracy of the analysis is demonstrated for a problem solved analytically by Koiter [5]and verified experimentally by Roorda [4].     

Behavior of reinforced concrete structures predicted by the finite element method

With current nonlinear analysis computer capabilities, considerable strides are being made in developing procedures, the utilization of which, allows one to analyze reinforced concrete structures while taking into account cracking and other characteristics of the constituent materials. Objective of the analyses is the determination of displacements as well as concrete and steel forces at various stages of loading. Cracking and the consequent loss of tensile strength is a major characteristic that must be modeled in any program for the analysis of reinforced concrete members. The three basic approaches have been employed by various investigators to account for tension cracking are discussed. Advantages and problems associated with these approaches are discussed. The formulation used to delineate compressive stress characteristics of concrete is evaluated. Solution procedures are described. Peculiarities required of solution methods in order to be suitable for the analysis of reinforced concrete systems are noted.     

A finite element approach to a quasi-variational inequality

We analyze the convergence of the finite element approximation to an elliptic one-dimensional quasi-variational inequality, connected to stochastic impulse control theory. We prove an optimal 0(h) error bound for the linear element solution of the associated variational selection. Then, by means of a continuity result, we derive anL ^∞-error estimate for the linear element solution of the quasi-variational inequality. Work supported by the Gruppo Nazionale per l'Analisi Matematica del C.N.R.     

A study of finite element and mathematical programming models for inelastic analysis of concrete framed structures

This paper presents an investigation of three analytical models for inelastic analysis of reinforced concrete framed structures. The first model employs a plane stress reinforced concrete element formulation with reinforcement oriented in any direction. The second model is based on a simplified layered frame element. The third model is a mathematical programming model in which the inelastic analysis is formulated as a linear complementarity problem. Formulation and significant computational steps of the three models are explained briefly. The performance of the three models in predicting the bending moment distribution at ultimate load stages is discussed through application to a number of frames and the results are compared with the experimental investigation conducted on 14 frames. This study concludes that the mathematical programming model is a computationally efficient model for inelastic analysis and offers scope for practical application for limit-state design of concrete frames.     

Nonlinear finite element analysis of shell structures using the semi-loof element

The Semi-Loof Shell element originally developed by Irons [2] for linear elastic analysis of thin shell structures is formulated to include large deflection and plastic deformation effects. In this paper the details of the finite element formulation of the problem using total Lagrangian coordinate systems are presented and different element matrices are given. For plastic materials following the Prandtl-Reuss flow rule with isotropic strain hardening a multi-layer approach using a subincremental technique is employed. Numerical results on the performance of the element for a variety of applications are presented. These computer studies include complete load-deflection curves into the post-buckling range and comparisons are made with other existing results. Current experience with the element indicates that it is a reliable and competitive element for nonlinear analysis of shells of general geometry.     

Limit load and shakedown analysis of plastic structures under stochastic uncertainty

Problems from plastic analysis are based on the convex, linear or linearised yield/strength condition and the linear equilibrium equation for the stress (state) vector. In practice one has to take into account stochastic variations of several model parameters. Hence, in order to get robust maximum load factors, the structural analysis problem with random parameters must be replaced by an appropriate deterministic substitute problem. A direct approach is proposed based on the primary costs for missing carrying capacity and the recourse costs (e.g. costs for repair, compensation for weakness within the structure, damage, failure, etc.). Based on the mechanical survival conditions of plasticity theory, a quadratic error/loss criterion is developed. The minimum recourse costs can be determined then by solving an optimisation problem having a quadratic objective function and linear constraints. For each vector a(·) of model parameters and each design vector x, one obtains then an explicit representation of the “best” internal load distribution F^∗. Moreover, also the expected recourse costs can be determined explicitly. Consequently, an explicit stochastic nonlinear program results for finding a robust maximal load factor μ^∗. The analytical properties and possible solution procedures are discussed.     

On the finite element creep rupture analysis of structures

The analysis of problems involving creep rupture is considered. Two creep material failure criteria are employed, i.e. the Kachanov-Rabotnov damage relations and a new, in conjunction with the finite element method, energy criterion.Calculations are reported for titanium notched tensile specimens, where the plastic strains are evaluated by the Ramberg-Osgood formulas.