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- Finite-Elemente-Methode (73) (remove)
The steel structure design codes require to check up the member strength when evaluating plastic deformations. The model of perfectly plastic material is accepted. The strength criteria for simple cross-sections (I section, etc.) of steel members are given in design codes. The analytical strength criteria for steel cross-sections and numerical approaches based on stepwise procedure are investigated in many articles. Another way for checking the carrying capacity of cross-sections is the use of methods that are applied for defining strain-deformed state of elastic perfectly plastic systems. In this paper non-iterative methods are suggested for checking strength of cross-sections. Carrying capacity of cross section is verified according to extremum principle of plastic fail under monotonically loading and the strain-deformed state of cross-section is defined according to extremum energy principals of elastic potential of residual stresses and complementary work of residual displacements. The mathematical expressions of these principals for discrete cross-section are formulated as problems of convex mathematical programming. The cross-section of steel member using finite element method is divided into free form plane elements. The constant distribution of stresses along the finite element is accepted. The relationships of finite elements for static formulation of the problem are formed so, that kinematics formulation relationships could be obtained in a formal way using the theory of duality. Numerical examples of determination of cross-section strength, composition of interactive curves and composition of moment-curvature curves for different axial force levels are presented.
Framed-tube system with multiple internal tubes is analysed using an orthotropic box beam analogy approach in which each tube is individually modelled by a box beam that accounts for the flexural and shear deformations, as well as the shear-lag effects. A simple numerical modeling technique is proposed for estimating the shear-lag phenomenon in tube structures with multiple internal tubes. The proposed method idealizes the framed-tube structures with multiple internal tubes as equivalent multiple tubes, each composed of four equivalent orthotropic plate panels. The numerical analysis is based on the minimum potential energy principle in conjunction with the variational approach. The shear-lag phenomenon of such structures is studied taking into account the additional bending moments in the tubes. A detailed work is carried out through the numerical analysis of the additional bending moment. The moment factor is further introduced to identify the shear lag phenomenon along with the additional moment.
The nonlinear behavior of concrete can be attributed to the propagation of microcracks within the heterogeneous internal material structure. In this thesis, a mesoscale model is developed which allows for the explicit simulation of these microcracks. Consequently, the actual physical phenomena causing the complex nonlinear macroscopic behavior of concrete can be represented using rather simple material formulations. On the mesoscale, the numerical model explicitly resolves the components of the internal material structure. For concrete, a three-phase model consisting of aggregates, mortar matrix and interfacial transition zone is proposed. Based on prescribed grading curves, an efficient algorithm for the generation of three-dimensional aggregate distributions using ellipsoids is presented. In the numerical model, tensile failure of the mortar matrix is described using a continuum damage approach. In order to reduce spurious mesh sensitivities, introduced by the softening behavior of the matrix material, nonlocal integral-type material formulations are applied. The propagation of cracks at the interface between aggregates and mortar matrix is represented in a discrete way using a cohesive crack approach. The iterative solution procedure is stabilized using a new path following constraint within the framework of load-displacement-constraint methods which allows for an efficient representation of snap-back phenomena. In several examples, the influence of the randomly generated heterogeneous material structure on the stochastic scatter of the results is analyzed. Furthermore, the ability of mesoscale models to represent size effects is investigated. Mesoscale simulations require the discretization of the internal material structure. Compared to simulations on the macroscale, the numerical effort and the memory demand increases dramatically. Due to the complexity of the numerical model, mesoscale simulations are, in general, limited to small specimens. In this thesis, an adaptive heterogeneous multiscale approach is presented which allows for the incorporation of mesoscale models within nonlinear simulations of concrete structures. In heterogeneous multiscale models, only critical regions, i.e. regions in which damage develops, are resolved on the mesoscale, whereas undamaged or sparsely damage regions are modeled on the macroscale. A crucial point in simulations with heterogeneous multiscale models is the coupling of sub-domains discretized on different length scales. The sub-domains differ not only in the size of the finite elements but also in the constitutive description. In this thesis, different methods for the coupling of non-matching discretizations - constraint equations, the mortar method and the arlequin method - are investigated and the application to heterogeneous multiscale models is presented. Another important point is the detection of critical regions. An adaptive solution procedure allowing the transfer of macroscale sub-domains to the mesoscale is proposed. In this context, several indicators which trigger the model adaptation are introduced. Finally, the application of the proposed adaptive heterogeneous multiscale approach in nonlinear simulations of concrete structures is presented.
To fulfil safety requirements the changes in the static and/or dynamic behaviour of the structure must be analysed with great care. These changes are often caused by local reduction of the stiffness of the structure caused by the irregularities in the structure, as for example cracks. In simple structures such analysis can be performed directly, by solving equations of motion, but for more complex structures a different approach, usually numerical, must be applied. The problem of crack implementation into the structure behaviour has been studied by many authors who have usually modelled the crack as a massless rotational spring of suitable stiffness placed at the beam at the location where the crack occurs. Recently, the numerical procedure for the computation of the stiffness matrix for a beam element with a single transverse crack has been replaced with the element stiffness matrix written in fully symbolic form. A detailed comparison of the results obtained by using 200 2D finite elements with those obtained with a single cracked beam element has confirmed the usefulness of such element.
A simple multiscale analysis framework for heterogeneous solids based on a computational homogenization technique is presented. The macroscopic strain is linked kinematically to the boundary displacement of a circular or spherical representative volume which contains the microscopic information of the material. The macroscopic stress is obtained from the energy principle between the macroscopic scale and the microscopic scale. This new method is applied to several standard examples to show its accuracy and consistency of the method proposed.
The displacements and stresses in arch dams and their abutments are frequently determined with 20-node brick elements. The elements are distorted near the contact plane between the wall and the abutment. A cantilever beam testbed has been developed to investigate the consequences of this distortion. It is shown that the deterioration of the accuracy in the computed stresses is significant. A compatible 18-node wedge element with linear stress variation is developed as an alternative to the brick element. The shape of this element type is readily adapted to the shape of the contact plane. It is shown that the accuracy of the computed stresses in the vicinity of the contact plane is improved significantly by the use of wedge elements.
This paper presents a novel numerical procedure based on the combination of an edge-based smoothed finite element (ES-FEM) with a phantom-node method for 2D linear elastic fracture mechanics. In the standard phantom-node method, the cracks are formulated by adding phantom nodes, and the cracked element is replaced by two new superimposed elements. This approach is quite simple to implement into existing explicit finite element programs. The shape functions associated with discontinuous elements are similar to those of the standard finite elements, which leads to certain simplification with implementing in the existing codes. The phantom-node method allows modeling discontinuities at an arbitrary location in the mesh. The ES-FEM model owns a close-to-exact stiffness that is much softer than lower-order finite element methods (FEM). Taking advantage of both the ES-FEM and the phantom-node method, we introduce an edge-based strain smoothing technique for the phantom-node method. Numerical results show that the proposed method achieves high accuracy compared with the extended finite element method (XFEM) and other reference solutions.
Global structural analyses in civil engineering are usually performed considering linear-elastic material behavior. However, for steel structures, a certain degree of plasticization depending on the member classification may be considered. Corresponding plastic analyses taking material nonlinearities into account are effectively realized using numerical methods. Frequently applied finite elements of two and three-dimensional models evaluate the plasticity at defined nodes using a yield surface, i.e. by a yield condition, hardening rule, and flow rule. Corresponding calculations are connected to a large numerical as well as time-consuming effort and they do not rely on the theoretical background of beam theory, to which the regulations of standards mainly correspond. For that reason, methods using beam elements (one-dimensional) combined with cross-sectional analyses are commonly applied for steel members in terms of plastic zones theories. In these approaches, plasticization is in general assessed by means of axial stress only. In this paper, more precise numerical representation of the combined stress states, i.e. axial and shear stresses, is presented and results of the proposed approach are validated and discussed.
For the analysis of arbitrary, by Finite Elements discretized shell structures, an efficient numerical simulation strategy with quadratic convergence including geometrically and physically nonlinear effects will be presented. In the beginning, a Finite-Rotation shell theory allowing constant shear deformations across the shell thickness is given in an isoparametric formulation. The assumed-strain concept enables the derivation of a locking-free finite element. The Layered Approach will be applied to ensure a sufficiently precise prediction of the propagation of plastic zones even throughout the shell thickness. The Riks-Wempner-Wessels global iteration scheme will be enhanced by a Line-Search procedure to ensure the tracing of nonlinear deformation paths with rather great load steps even in the post-peak range. The elastic-plastic material model includes isotropic hardening. A new Operator-Split return algorithm ensures considerably exact solution of the initial-value problem even for greater load steps. The combination with consistently linearized constitutive equations ensures quadratic convergence in a close neighbourhood to the exact solution. Finally, several examples will demonstrate accuracy and numerical efficiency of the developed algorithm.
A geometrical inclusion-matrix model for the finite element analysis of concrete at multiple scales
(2003)
This paper introduces a method to generate adequate inclusion-matrix geometries of concrete in two and three dimensions, which are independent of any specific numerical discretization. The article starts with an analysis on shapes of natural aggregates and discusses corresponding mathematical realizations. As a first prototype a two-dimensional generation of a mesoscale model is introduced. Particle size distribution functions are analysed and prepared for simulating an adequate three-dimensional representation of the aggregates within a concrete structure. A sample geometry of a three-dimensional test cube is generated and the finite element analysis of its heterogeneous geometry by a uniform mesh is presented. Concluding, aspects of a multiscale analysis are discussed and possible enhancements are proposed.