The simulation of sheet metal forming processes via integrating solid-shell element with explicit finite element method

Solid-shell elements can be seen as a class of typical double-surfaced shell elements with no rational degrees of freedom, which are more suitable for analyzing double-sided contact problems than conventional shell elements. In this study, a solid-shell finite element model is implemented into the explicit finite element software ABAQUS/Explicit as a user-defined element, through which the sheet metal forming processes are simulated. The main feature of this finite element model is that the solid-shell element formulation is embedded into an explicit finite element procedure, compared to the previous studies on the solid-shell elements under the implicit finite element framework. To obtain a straightforward element, a complete integration scheme is adopted. No loss of generality, a twelve-parameter enhance assumed strain method is employed to improve the element’s behavior. Two benchmarks from the NUMISHEET conference and a U-channel roll-forming process are simulated with this explicit solid-shell finite element model. The calculated results are comparable with experimental and numerical results presented in the literatures.     

A reduced integration finite element technology based on a thermomechanically consistent stabilisation for 3D problems

In this paper we suggest a new finite element technology for thermomechanically fully coupled problems. It is based on the method of reduced integration with hourglass stabilisation. The proposed formulation allows the evaluation of the additional thermal field at one Gauss point, e.g. in the centre of the element. One crucial aspect is the Taylor expansion of all constitutively dependent variables, as e.g. the heat flux, the internal and the external rates of dissipation, with respect to the centre of the element. In this way a so-called thermal hourglass stabilisation, analogously to the classical mechanical hourglass stabilisation, is derived. The thermal stabilisation parameters are defined well and the computational efficiency which comes along with the consistent formulation is very high. The new element formulation is applied on thermomechanically coupled problems of finite elastoplasticity. It can be also easily used in the context of other multi-field problems.     

An elasto-plastic rate-dependent finite element analysis of the metal forming process

An elasto-plastic rate-dependent finite element formulation is developed into the solution of the large strain and deformation problem. The formation is based on the power form constitutive equation for the stress-strain-strain rate relation of the material. A simple one-step Euler's time integration scheme is adopted to automatically control the time increment. After incorporating a force rate term which is due to the effect of the strain rate, the simulation is completed by modifying the updated Lagrangian formulation. The numerical results can be used as options in the selection of the adequate tool speed, die geometry, and die material.     

Computer-aided engineering for sheet metal forming: definition of a springback quality function

Computer-aided engineering methods are extensively applied to sheet metal forming integrated design. The adoption of a new class of materials, the advanced high strength steels, has increased the occurrence of springback, and consequently the request for tools oriented to springback reduction and optimization. This paper presents an approximated formulation to compute the springback field after stamping through the finite element analysis of the process. This can be found assuming that the residual field of nodal forces after stamping produces a springback shape referable to a linear combination of n modes of vibration of the nominal shape of the component. The aim of this formulation is not that of substituting the finite element analysis of the springback but rather to make use of the coefficients of the linear combination, so to define a global quality function for springback. In this way, Robust Design methods or other current optimization procedures to improve the stamping process as for structural defects (such wrinkling, necking and flatness) can be applied also for the reduction of springback. The meaning of these coefficients will be shown through three test cases and the consistency of the formulation will be discussed according to the number of modes of vibration included in the computation.     

Estimation of forming limit diagrams by the use of the finite element method and Monte Carlo simulation

A stochastic finite element-based approach for forming limit calculations of sheets is proposed and evaluated. Material inhomogeneities are represented by spatial thickness variations of the sheet which are modelled by the use of random fields. The effects of changing the smoothness, wavelengths, amplitude and anisotropy of the field realisations on the forming limit diagram are investigated. Further, the effects of the patch size and plastic anisotropy on the forming limit diagram are studied. The assumed thickness variations result in a quite wide scatter band, and changes of the characteristics of the thickness field result in changes of the shape and variance of the forming limit diagram.     

Scalable uncertainty and reliability analysis by integration of advanced Monte Carlo simulation and generic finite element solvers

This contribution describes how the uncertainty associated with structures can be modeled and analyzed, in context with state-of-the-art FE software and modern computing infrastructure. Uncertainty modeling with high-dimensional random variables and random fields motivates the adoption of advanced Monte Carlo methods for reliability analysis. On the implementation side, object-orientation and parallelization have been embraced to ensure flexibility and performance.A novel, Matlab-based toolkit, COSSAN-X, embodying these characteristics, is presented. The application to a satellite under harmonic excitation and a turbine blade under centrifugal loading indicates the importance of considering spatial fluctuations and the scalability with respect to realistic FE models.     

Development of parallel explicit finite element sheet forming simulation system based on GPU architecture

Sheet forming simulation is very important for vehicle body design. Due to the increase of complexity and scale of the CAE model, a tradeoff between the accuracy and efficiency become the bottleneck for application. Therefore, a parallel explicit finite element (FE) based on graphics processing unit (GPU) architecture for sheet forming is developed. Implementation details with computer unified device architecture (CUDA) are considered in this work. A pre-index strategy is suggested for parallelization of nodal force assembling. Parallel reduction method is introduced to calculation of the global time step. To ensure the reliability and accuracy of the GPU-based program, double precision floating and intrinsic functions are implemented for the explicit FE computing. The simulation results based on a commercial NVIDIA GTX285 device can obtain about 27X speedup than on a Intel Q8200 CPU, which demonstrates the efficiency of the parallel sheet forming simulation system.     

Approximation of a second order Stefan-like problem by means of a finite element method

The paper deals with the space semidiscretization of a Stefan-like problem of the second order by means of finite elements. The convergence of the approximated solution to the solution of the continuous problem and an estimate of the rate of convergence are proved. Lavoro svolto nell'ambito dell'attività del G.N.I.M. e del I.A.N. del C.N.R. di Pavia.     

Integration of feedforward neural network and finite element in the draw-bend springback prediction

To achieve accurate results, current nonlinear elastic recovery applications of finite element (FE) analysis have become more complicated for sheet metal springback prediction. In this paper, an alternative modelling method able to facilitate nonlinear recovery was developed for springback prediction. The nonlinear elastic recovery was processed using back-propagation networks in an artificial neural network (ANN). This approach is able to perform pattern recognition and create direct mapping of the elastically-driven change after plastic deformation. The FE program for the sheet metal springback experiment was carried out with the integration of ANN. The results obtained at the end of the FE analyses were found to have improved in comparison to the measured data.     

On near equivalence of assumed stress and reduced integration formulations of the bilinear plane stress finite element

It is now well known that displacement finite elements in which reduced integration is used tend to exhibit similar performance to that of finite elements formulated on a stress basis. The bilinear displacement element for plane stress provides a useful example of this equivalence; as when selective one point integration is used for the shearing energy, the resulting stiffness matrix is identical to that obtained for the equivalent assumed stress element when Poisson's ratio is zero.     

Simplified ultimate load analysis by means of the finite element method

The ultimate load carrying capacity of cellular structures is predicted by means of a simplified procedure based on the Finite Element Method. The local stiffnesses are divided into the following linear regions: pre-critical, post-critical pre-collapse and post-collapse. The method is demonstrated on two double bottom structures.     

Solution of the Boussinesq equations by means of the finite element method

A finite element method is presented for the computation of flows that are influenced by buoyancy forces. The accuracy of several finite elements is studied by solving the Bénard problem and determining the critical Rayleigh number. It is found that the accuracy is greatly enhanced if the shape functions satisfy a certain requirement that arises from the physical nature of the problem.     

Application of finite differences for solving the two-dimensional elasticity problem by means of the finite element method

Finite differences are applied to simplify the finite element method of solving the two-dimensional elasticity problem. Derivatives are replaced by difference quotients so that the only degrees of freedom are the values of the function at the nodes. Numerical examples are included.     

Three dimensional modeling and finite element simulation of a generic end mill

The geometry of cutting flutes and the surfaces of end mills is one of the crucial parameters affecting the quality of the machining in the case of end milling. These are usually represented by two-dimensional models. This paper describes in detail the methodology to model the geometry of a flat end mill in terms of three-dimensional parameters. The geometric definition of the end mill is developed in terms of surface patches; flutes as helicoidal surfaces, the shank as a surface of revolution and the blending surfaces as bicubic Bezier and biparametric sweep surfaces. The proposed model defines the end mill in terms of three-dimensional rotational angles rather than the conventional two dimensional angles. To validate the methodology, the flat end milling cutter is directly rendered in OpenGL environment in terms of three-dimensional parameters. Further, an interface is developed that directly pulls the proposed three-dimensional model defined with the help of parametric equations into a commercial CAD modeling environment. This facilitates a wide range of downstream technological applications. The modeled tool is used for finite element simulations to study the cutting flutes under static and transient dynamic load conditions. The results of stress distribution (von mises stress), translational displacement and deformation are presented for static and transient dynamic analysis for the end mill cutter flute and its body. The method described in this paper offers a simple and intuitive way of generating high-quality end mill models for use in machining process simulations. It can be easily extended to generate other tools without relying on analytical or numerical formulations.     

Color computer graphics in magnetic field analysis by means of the finite element method

The finite element method for electromagnetic fields is very popular because of its powerful numerical techniques. Since the output from the finite element analyses (F.E.A.) usually makes a pile of numerical data, it is very important to display them intelligibly and accurately in order to assist analysts in understanding and evaluating the results. Three post-processing methods in the F.E.A. using a multi-color pen plotter or a color CRT are proposed: (1) Depiction of magnetic flux lines in two or three dimensional fields by using a multi-color pen plotter, (2) Depiction of magnetic flux density distribution with flux lines in two dimensional fields by using a color CRT, (3) Depiction of error distribution by using a color CRT.

By using these three methods analysts can visually grasp the behavior of the magnetic fields and the error distribution in detail.     

Improving satellite images classification using remote and ground data integration by means of stochastic simulation

A methodology is proposed, to assess land surface cover classification using a geostatistical methodology of stochastic simulation, direct sequential cosimulation, to combine field observations with remotely sensed data classified with the classical algorithm of maximum likelihood classification. This procedure has two main advantages: (1) incorporation of a spatial continuity statistics; and (2) integration of different scales of information, contained in polygons (training areas) and point information (field observations), which also involves different qualities of information that is less reliable and more reliable, respectively. Moreover, this methodology allows production not only of a classified map, but also of maps of occupation proportions and of uncertainty for each thematic class. Local co‐regionalization models are applied to account for local differences in both field data availability and distribution, and the correlation between these hard data and the classified satellite images as soft data. The methodology is based on two criteria: the influence of the hard data dependent on their availability and proportional to their proximity; and the influence of the soft data dependent on their local correlation to the hard data. The method is applied to a study of four economically important forest tree species on the Setúbal Peninsula (south of Lisbon, Portugal). The results show more contiguous forest covers, i.e. more spatial contiguity, than the classical classification. In comparison to a contemporary field inventory, the proposed method improved forest cover estimations, showing a difference of only 3%.     

Mathematical modelling and finite element simulation of smart tubular composites

This paper presents a mathematical modelling and numerical simulation method for three-dimensional smart tubular 1(0)-3 composites based on a representative composite volume (RCV) approach. For the problems we consider, numerical results show that the maximum mechanical displacement varies linearly with the applied electrical potential and grows nonlinearly with increasing the RCV height. Further, we observe that decreasing the distance between the inner and outer radii results in increasing the maximum displacement. This refers to composites with large Young’s modulus of the polymer phase, whereas for “soft” polymers (i.e. for Young’s modulus of the polymers of order less than GPa) no particular ‘rule’ is evident, in which case the Poisson’s ratio is the most important parameter.     

Three-dimensional finite element simulation of three-phase flow in a deforming fissured reservoir

The development of a capacity to predict the exploitation of structurally complicated and fractured oil reservoirs is essential for the rational use of investment capital. A poor understanding of how the reservoir behaves during production may lead to inept, costly and inefficient development schemes. The mathematical formulation of a three-phase, three-dimensional fluid flow and rock deformation in fractured reservoirs is hence presented. The present formulation, consisting of both the equilibrium and multiphase mass conservation equations, accounts for the significant influence of coupling between the fluid flow and solid deformation, an aspect usually ignored in the reservoir simulation literature. A Galerkin-based finite element method is applied to discretise the governing equations in space and a finite difference scheme is used to march the solution in time. The final set of equations, which contain the additional cross coupling terms as compared to similar existing models, are highly non-linear and the elements of the coefficient matrices are updated implicitly during each iteration in terms of the independent variables. A field scale example is employed as an alpha case to test the validity and robustness of the currently formulation and numerical scheme. The results illustrate a significantly different behaviour for the case of a reservoir where the impact of coupling is also considered.