Th. Zimmermann

Object-oriented non-linear finite element analysis: Application to J2 plasticity

Abstract The object-oriented programming concept is applied to the finite element method for non-linear static analysis. Starting from an existing linear object-oriented environment, the question whether the object-oriented approach can be suitably extended to situations where the algorithmic procedure is dominant is examined. The Newton-Raphson and the stress-integration algorithms are presented along with the necessary extensions to the existing objects. The implementation in C+ + is described. The advantage of object-oriented programming is demonstrated, in particular through the concept of non-anticipation of the state of the object.

Dynamic rupture analysis of reinforced concrete shells

Abstract Extreme dynamic loading conditions often require the rupture analysis of reinforced and prestressed-concrete structures. The study presented in this paper extends a method of analysis of dynamic loading conditions which has proven efficient for short- and long-time loads. Another aim is to adapt the method to thin-walled structures. It is not sufficient to work only with plastic rupture and yield surfaces locally which are compared to the elastic distribution of the stress resultants; it is essential to account for the redistribution of the latter. The method proposed consists of discretizing the structure into isoparametric three-dimensional elements with 20 nodes for the concrete and one-dimensional bar elements with three nodes for the steel. The latter can also be handled with a ‘smeared’ two-dimensional membrane element. In compression a three-dimensional non-linear elastic constitutive law is introduced for the concrete, and a triaxial failure surface expressed in the stress invariants is used, determining cracking and crushing. Two- and three-dimensional cracking surfaces in which no components of stress are transmitted are accounted for. The possibility exists that, during the history of loading, cracks can close up again. For steel, a yield criterion is selected. The non-linear analysis is based on the concept of initial stress. Residual loads are calculated using information in Gauss integration points. The ultimate load is reached when the algorithm does not converge. The corresponding failure modes can be interpreted as those for which a state of equilibrium is no longer possible. The equations of motion are discretized in time, using an extension of the linear acceleration method. As in the static case, several iterations are necessary to reduce the residual load vector to a negligible quantity. A built-in circular plate is analyzed for an evenly distributed load. The results with one and several isoparametric elements in width are compared to the solution determined with the classical yield line theory. Cracks in the concrete and yielding of the steel in both directions are properly represented. In the non-linear domain moment redistribution is observed which allows for a substantial increase in the ultimate load. All states of material behaviour are observed in the final stage. A thin-walled shell consisting of a cylinder and a sphere is also examined for a non-symmetric loading involving the interaction of membrane and bending behaviour. A dynamic non-linear analysis is performed for this load, which represents the impact of an airplane on the external shield building of a nuclear power plant. The non-linear analysis does allow for a substantial saving of reinforcement steel compared to the standard design procedure. Conclusions which include pitfalls, shortcomings and suggestions for future research are specified.

Object-oriented finite elements I. Principles of symbolic derivations and automatic programming

Abstract The development of a numerical finite element model for a given initial-boundary-value problem goes essentially through the derivation of a weak form, its discretization and finally the derivation of the matrix forms. These steps can, to a large extent, be automated, except for the ones which require intelligence or some form of decision making from the developer. The article outlines the essential steps of an interactive quasi-automatic approach and illustrates it in the example of a linear uniaxial bar formulation for dynamics. The implementation is done in SmalltalkV. A detailed description of the proposed environment is described in a companion article.

Object-oriented finite elements III. Theory and application of automatic programming

In a first paper [1], the authors have developed the key features of an object-oriented environment for the symbolic derivation of linear initial-boundary-value problems. The approach was illustrated on a simple example of an elastic bar in dynamics. In a companion paper [2], the structure of the proposed environment was described at length. In this article, the key features of the automatic generation of finite elements in a symbolic object-oriented environment are given. A few examples of derivation and automatic programming are developed and numerically tested. First, a classical Galerkin formulation of Stokes flow is compared to a Galerkin least-squares stabilization formulation. Then, various stabilized formulations are tested on a simple scalar diffusion model equation.

Aspects of an object-oriented finite element environment

Abstract The object-oriented approach provides an appropriate context for an integrated description of finite element related techniques within a single unified environment, combining symbolic and numerical manipulations, graphics and expertise. This paper discusses and illustrates the key features of such an integrated environment which includes an object-oriented graphic interactive environment, object-oriented operators for symbolic mathematical derivations, an object-oriented finite element environment, and its extension to object-oriented knowledge based expert assistance.

Object-oriented finite elements. IV. Symbolic derivations and automatic programming of nonlinear formulations

Reference EPFL-ARTICLE-102770View record in Web of Science Record created on 2007-04-23, modified on 2016-08-08

Failure and fracturing analysis of concrete structures

Abstract Some aspects of fracture analysis of concrete structures are discussed in this article. In particular it is shown that when localized failure occurs (by macrofracture propagation or localization of strain) structural size effects come into play. Mesh dependent finite element solutions are then observed unless size effects are correctly accounted for. Tensile fracture is examined first. The “classical” discrete and smeared crack approaches are reviewed and their extension to nonlinear fracture models like the fictitious crack model and the crack band model is illustrated. The smeared crack approach coupled first with a tensile strength criterion, second with a linear elastic fracture mechanics criterion is then applied to the failure mode analysis of a PCRV. Plastic fracturing with localization into shear bands, strain softening, mesh dependence and its correction are examined next. The use of plasticity for tensile fracture simulation is also discussed. Finally numerical difficulties inherent to the modeling of softening behavior are investigated.

Aircraft impact on reinforced concrete shells influence of material nonlinearities on equipment response spectra

Abstract The effects of material nonlinearities on response spectra resulting from the impact of a commercial aircraft on the secondary containment of a BWR reactor are investigated. A unite element model taking into account concrete cracking and crushing and steel yielding is used for the analysis. The results show that, for the design considered here, no reduction of the response spectra due to material nonlinearity in the impact zone can be expected. As a matter of fact, an amplification results close to the impact area.

Three-dimensional rupture analysis of a prestressed concrete pressure vessel including creep effects

Abstract This paper describes briefly the results obtained from a nonlinear analysis up to rupture of a PCRV taking into account creep effects. This analysis aims mainly at evaluating the influence of the redistribution of stresses due to the rheological behavior of concrete on the rupture pressure of a PCRV. First, the method of nonlinear analysis for creep and rupture is described briefly. The mathematical model, of a general application, is based on the finite element method, utilizing the isoparametric elements. Nonlinearities are introduced by the use of iterative techniques. It allows us to predict, within satisfactory limits, the behavior of massive prestressed concrete structures loaded up to destruction. The use of classical parameters for definition of the physical characteristics of materials for formulating the constitutive laws makes the model particularly interesting for practical applications. The analysis of the PCRV for a gas-cooled fast reactor developed by the Swiss Federal Institute for Reactor Research is also presented. This PCRV has large cavities in its walls to house direct cycle gas turbines and other mechanical equipment. First, the creep analysis is carried out taking account of the envisaged construction schedule and the loading during the testing period and finally during the normal exploitation of the PCRV. Proceeding from the state of stress obtained as such the rupture analysis is carried out for a sudden increase of internal pressure and temperature gradient due to a hypothetical accident.

Stabilized Finite Element Applications in Geomechanics

Locking phenomena and pressure oscillations are often associated with the use of low order elements to simulate incompressible or dilatant behavior, typical of geomechanical applications. A stabilized Galerkin Least-Squares formulation (GLS), along the lines advocated by Hughes et al (1986) for fluid mechanics, is extended in this paper to a mixed displacement-pressure formulation of elastoplasticity. Applications in geomechanics demonstrate that the proposed formulation provides an appropriate and general solution to overcome locking phenomena.