A C1 finite element for Kirchhoff plate bending

After a short introduction the possibilities and limitations of polynomial simple elements with C1 continuity are discussed with reference to plate bending analysis. A family of this kind of elements is presented.. These elements are applied to simple cases in order to assess their computational efficiency. Finally some conclusions are shown, and future research is also proposed.

Some consistent finite element formulations of 1-D beam models: a comparative study

A consistent Finite Element formulation was developed for four classical 1-D beam models. This formulation is based upon the solution of the homogeneous differential equation (or equations) associated with each model. Results such as the shape functions, stiffness matrices and consistent force vectors for the constant section beam were found. Some of these results were compared with the corresponding ones obtained by the standard Finite Element Method (i.e. using polynomial expansions for the field variables). Some of the difficulties reported in the literature concerning some of these models may be avoided by this technique and some numerical sensitivity analysis on this subject are presented.

Two-dimensional isostatic meshes in the finite element method

In a Finite Element (FE) analysis of elastic solids several items are usually considered, namely, type and shape of the elements, number of nodes per element, node positions, FE mesh, total number of degrees of freedom (dot) among others. In this paper a method to improve a given FE mesh used for a particular analysis is described. For the improvement criterion different objective functions have been chosen (Total potential energy and Average quadratic error) and the number of nodes and dof's of the new mesh remain constant and equal to the initial FE mesh. In order to find the mesh producing the minimum of the selected objective function the steepest descent gradient technique has been applied as optimization algorithm. However this efficient technique has the drawback that demands a large computation power. Extensive application of this methodology to different 2-D elasticity problems leads to the conclusion that isometric isostatic meshes (ii-meshes) produce better results than the standard reasonably initial regular meshes used in practice. This conclusion seems to be independent on the objective function used for comparison. These ii-meshes are obtained by placing FE nodes along the isostatic lines, i.e. curves tangent at each point to the principal direction lines of the elastic problem to be solved and they should be regularly spaced in order to build regular elements. That means ii-meshes are usually obtained by iteration, i.e. with the initial FE mesh the elastic analysis is carried out. By using the obtained results of this analysis the net of isostatic lines can be drawn and in a first trial an ii-mesh can be built. This first ii-mesh can be improved, if it necessary, by analyzing again the problem and generate after the FE analysis the new and improved ii-mesh. Typically, after two first tentative ii-meshes it is sufficient to produce good FE results from the elastic analysis. Several example of this procedure are presented.

A two-dimensional finite element model of front surface current flow in cells under non-uniform, concentrated illumination

A two-dimensional finite element model of current flow in the front surface of a PV cell is presented. In order to validate this model we perform an experimental test. Later, particular attention is paid to the effects of non-uniform illumination in the finger direction which is typical in a linear concentrator system. Fill factor, open circuit voltage and efficiency are shown to decrease with increasing degree of non-uniform illumination. It is shown that these detrimental effects can be mitigated significantly by reoptimization of the number of front surface metallization fingers to suit the degree of non-uniformity. The behavior of current flow in the front surface of a cell operating at open circuit voltage under non-uniform illumination is discussed in detail.

Simulation of Freight Trains Equipped with Partially Filled Tank Containers and Related Resonance Phenomenon

To study the fluid motion-vehicle dynamics interaction, a model of four, liquid filled two-axle container freight wagons was set up. The railway vehicle has been modelled as a multi-body system (MBS). To include fluid sloshing, an equivalent mechanical model has been developed and incorporated. The influence of several factors has been studied in computer simulations, such as track defects, curve negotiation, train velocity, wheel wear, liquid and solid wagonload, and container baffles. SIMPACK has been used for MBS analysis, and ANSYS for liquid sloshing modelling and equivalent mechanical systems validation. Acceleration and braking manoeuvres of the freight train set the liquid cargo into motion. This longitudinal sloshing motion of the fluid cargo inside the tanks initiated a swinging motion of some components of the coupling gear. The coupling gear consists of UIC standard traction hooks and coupling screws that are located between buffers. One of the coupling screws is placed in the traction hook of the opposite wagon thus joining the two wagons, whereas the unused coupling screw rests on a hanger. Simulation results showed that, for certain combinations of type of liquid, filling level and container dimensions, the liquid cargo could provoke an undesirable, although not hazardous, release of the unused coupling screw from its hanger. The coupling screw's release was especially obtained when a period of acceleration was followed by an abrupt braking manoeuvre at 1 m/s2. It was shown that a resonance effect between the liquid's oscillation and the coupling screw's rotary motion could be the reason for the coupling screw's undesired release. Possible solutions to avoid the phenomenon are given.Acceleration and braking manoeuvres of the freight train set the liquid cargo into motion. This longitudinal sloshing motion of the fluid cargo inside the tanks initiated a swinging motion of some components of the coupling gear. The coupling gear consists of UIC standard traction hooks and coupling screws that are located between buffers. One of the coupling screws is placed in the traction hook of the opposite wagon thus joining the two wagons, whereas the unused coupling screw rests on a hanger. This paper reports on a study of the fluid motion-train vehicle dynamics interaction. In the study, a model of four, liquid-filled two-axle container freight wagons was developed. The railway vehicle has been modeled as a multi-body system (MBS). To include fluid sloshing, an equivalent mechanical model has been developed and incorporated. The influence of several factors has been studied in computer simulations, such as track defects, curve negotiation, train velocity, wheel wear, liquid and solid wagonload, and container baffles. A simulation program was used for MBS analysis, and a finite element analysis program was used for liquid sloshing modeling and equivalent mechanical systems validation. Acceleration and braking maneuvers of the freight train set the liquid cargo into motion. This longitudinal sloshing motion of the fluid cargo inside the tanks initiated a swinging motion of some components of the coupling gear. Simulation results showed that, for certain combinations of type of liquid, filling level and container dimensions, the liquid cargo could provoke an undesirable, although not hazardous, release of an unused coupling screw from its hanger. It was shown that a resonance effect between the liquid's oscillation and the coupling screw's rotary motion could be the reason for the coupling screw's undesired release. Solutions are suggested to avoid the resonance problem, and directions for future research are given.

Elastoplastic consolidation at finite strain. Part 2: finite element implementation and numerical examples

A mathematical model for finite strain elastoplastic consolidation of fully saturated soil media is implemented into a finite element program. The algorithmic treatment of finite strain elastoplasticity for the solid phase is based on multiplicative decomposition and is coupled with the algorithm for fluid flow via the Kirchhoff pore water pressure. A two-field mixed finite element formulation is employed in which the nodal solid displacements and the nodal pore water pressures are coupled via the linear momentum and mass balance equations. The constitutive model for the solid phase is represented by modified Cam—Clay theory formulated in the Kirchhoff principal stress space, and return mapping is carried out in the strain space defined by the invariants of the elastic logarithmic principal stretches. The constitutive model for fluid flow is represented by a generalized Darcy's law formulated with respect to the current configuration. The finite element model is fully amenable to exact linearization. Numerical examples with and without finite deformation effects are presented to demonstrate the impact of geometric nonlinearity on the predicted responses. The paper concludes with an assessment of the performance of the finite element consolidation model with respect to accuracy and numerical stability.

Modelling of corrosion-induced cover cracking in reinforced concrete by an embedded cohesive crack finite element

Corrosion of a reinforcement bar leads to expansive pressure on the surrounding concrete that provokes internal cracking and, eventually, spalling and delamination. Here, an embedded cohesive crack 2D finite element is applied for simulating the cracking process. In addition, four simplified analytical models are introduced for comparative purposes. Under some assumptions about rust properties, corrosion rate, and particularly, the accommodation of oxide products within the open cracks generated in the process, the proposed FE model is able to estimate time to surface cracking quite accurately. Moreover, emerging cracking patterns are in reasonably good agreement with expectations. As a practical case, a prototype application of the model to an actual bridge deck is reported.

A three-dimensional self-adaptive hp finite element method for the characterization of waveguide discontinuities

We propose the use of a highly-accurate three-dimensional (3D) fully automatic hp-adaptive finite element method (FEM) for the characterization of rectangular waveguide discontinuities. These discontinuities are either the unavoidable result of mechanical/electrical transitions or deliberately introduced in order to perform certain electrical functions in modern communication systems. The proposed numerical method combines the geometrical flexibility of finite elements with an accuracy that is often superior to that provided by semi-analytical methods. It supports anisotropic refinements on irregular meshes with hanging nodes, and isoparametric elements. It makes use of hexahedral elements compatible with high-order H(curl)H(curl) discretizations. The 3D hp-adaptive FEM is applied for the first time to solve a wide range of 3D waveguide discontinuity problems of microwave communication systems in which exponential convergence of the error is observed.

Load displacement in grape harvesters: Discrete Element Analysis.

Dynamic weighing of the hopper in grape harvesters is affected by a number of factors. One of them is the displacement of the load inside the hopper as a consequence of the terrain topography. In this work, the weight obtained by a load cell in a grape harvester has been analysed and quantified using the discrete element method (DEM). Different models have been developed considering different scenarios for the terrain.

Simplified Finite Element Assessment of Beams With and Without Shear Deformation

This paper presents a simplified finite element (FE) methodology for solving accurately beam models with (Timoshenko) and without (Bernoulli-Euler) shear deformation. Special emphasis is made on showing how it is possible to obtain the exact solution on the nodes and a good accuracy inside the element. The proposed simplifying concept, denominated as the equivalent distributed load (EDL) of any order, is based on the use of Legendre orthogonal polynomials to approximate the original or acting load for computing the results between the nodes. The 1-span beam examples show that this is a promising procedure that allows the aim of using either one FE and an EDL of slightly higher order or by using an slightly larger number of FEs leaving the EDL in the lowest possible order assumed by definition to be equal to 4 independently of how irregular the beam is loaded.

Finite element simulation of sandwich panels of plasterboard and rock wool under mixed mode fracture

This paper presents the results of research on mixed mode fracture of sandwich panels of plasterboard and rock wool. The experimental data of the performed tests are supplied. The specimens were made from commercial panels. Asymmetrical three-point bending tests were performed on notched specimens. Three sizes of geometrically similar specimens were tested for studying the size effect. The paper also includes the numerical simulation of the experimental results by using an embedded cohesive crack model.The involved parameters for modelling are previously measured by standardised tests.

An application of the finite element method to curve fitting

An application of the Finite Element Method (FEM) to the solution of a geometric problem is shown. The problem is related to curve fitting i.e. pass a curve trough a set of given points even if they are irregularly spaced. Situations where cur ves with cusps can be encountered in the practice and therefore smooth interpolatting curves may be unsuitable. In this paper the possibilities of the FEM to deal with this type of problems are shown. A particular example of application to road planning is discussed. In this case the funcional to be minimized should express the unpleasent effects of the road traveller. Some comparative numerical examples are also given.

Two-dimensional mesh optimization in the finite element method

The solution to the problem of finding the optimum mesh design in the finite element method with the restriction of a given number of degrees of freedom, is an interesting problem, particularly in the applications method. At present, the usual procedures introduce new degrees of freedom (remeshing) in a given mesh in order to obtain a more adequate one, from the point of view of the calculation results (errors uniformity). However, from the solution of the optimum mesh problem with a specific number of degrees of freedom some useful recommendations and criteria for the mesh construction may be drawn. For 1-D problems, namely for the simple truss and beam elements, analytical solutions have been found and they are given in this paper. For the more complex 2-D problems (plane stress and plane strain) numerical methods to obtain the optimum mesh, based on optimization procedures have to be used. The objective function, used in the minimization process, has been the total potential energy. Some examples are presented. Finally some conclusions and hints about the possible new developments of these techniques are also given.

A dynamic programming approach to the formulation and solution of finite element equations

A method for formulating and algorithmically solving the equations of finite element problems is presented. The method starts with a parametric partition of the domain in juxtaposed strips that permits sweeping the whole region by a sequential addition (or removal) of adjacent strips. The solution of the difference equations constructed over that grid proceeds along with the addition removal of strips in a manner resembling the transfer matrix approach, except that different rules of composition that lead to numerically stable algorithms are used for the stiffness matrices of the strips. Dynamic programming and invariant imbedding ideas underlie the construction of such rules of composition. Among other features of interest, the present methodology provides to some extent the analyst's control over the type and quantity of data to be computed. In particular, the one-sweep method presented in Section 9, with no apparent counterpart in standard methods, appears to be very efficient insofar as time and storage is concerned. The paper ends with the presentation of a numerical example

Finite element simulation of dispersion in the Bay of Santander

Two mathematical models are used to simulate pollution in the Bay of Santander. The first is the hydrodynamic model that provides the velocity field and height of the water. The second gives the pollutant concentration field as a resultant. Both models are formulated in two-dimensional equations. Linear triangular finite elements are used in the Galerkin procedure for spatial discretization. A finite difference scheme is used for the time integration. At each time step the calculated results of the first model are input to the second model as field data. The efficiency and accuracy of the models are tested by their application to a simple illustrative example. Finally a case study in simulation of pollution evolution in the Bay of Santander is presented