ANN approach to sorption hysteresis within a coupled hygro‐thermo‐mechanical FE analysis

Non‐linear deformable porous media with sorption (capillary condensation) hysteresis are considered. An artificial neural network with two hidden layers is trained to interpolate the sorption hysteresis using a set of experimental data. The performance of the ANN, which is applied as a procedure in the FE code, is investigated, both from numerical, as well as from physical viewpoint. The ANN‐FE code has been developed and tested for 1‐D and 2‐D problems concerning cyclic wetting–drying of concrete elements. In general, the application of the ANN procedure inside the classical FE program does not have any negative effect on the numerical performance of the code. The results obtained indicate that the sorption isotherm hysteresis is of importance during analysis of hygrothermal and mechanical behaviour of capillary‐porous materials. The most distinct differences are observed for the saturation and displacement solutions. The ANN‐FE approach seems to be an efficient way to take into account the influence of hysteresis during analysis of hygro‐thermal behaviour of capillary‐porous materials. Copyright © 2001 John Wiley & Sons, Ltd.     

Finite element formulation for anisotropic coupled piezoelectro‐hygro‐thermo‐viscoelasto‐dynamic problems

A finite element algorithm has been developed for the efficient analysis of smart composite structures with piezoelectric polymer sensors or/and actuators based on piezoelectro‐hygro‐thermo‐viscoelasticity. Variational principles for anisotropic coupled piezoelectro‐hygro‐thermo‐viscoelasto‐dynamic problems have also been proposed in this study. As illustrative studies, dynamic responses in laminated composite beams and plates with PVDF sensors and actuators are obtained as functions of time using the present finite element procedures. The voltage feedback control scheme is utilized. The proposed numerical method can be used for analysing problems in the design of smart structures as well as smart sensors and actuators. Copyright © 1999 John Wiley & Sons, Ltd.     

An evaluation of limited‐memory sparse linear solvers for thermo‐mechanical applications

We consider the performance of sparse linear solvers for problems that arise from thermo‐mechanical applications. Such problems have been solved using sparse direct schemes that enable robust solution at the expense of memory requirements that grow non‐linearly with the dimension of the coefficient matrix. In this paper, we consider a class of preconditioned iterative solvers as a limited‐memory alternative to direct solution schemes. However, such preconditioned iterative solvers typically exhibit complex trade‐offs between reliability and performance. We therefore characterize such trade‐offs for systems from thermo‐mechanical problems by considering several preconditioning schemes including multilevel methods and those based on sparse approximate inversion and incomplete matrix factorization. We provide an analysis of computational costs and memory requirements for model thermo‐mechanical problems, indicating that certain incomplete factorization schemes can achieve good performance. We also provide empirical evaluations that corroborate our analysis and indicate the relative effectiveness of different solution schemes. Our results indicate that our drop‐threshold incomplete Cholesky preconditioning is more robust, efficient and flexible than other popular preconditioning schemes. In addition, we propose preconditioner reuse to amortize preconditioner construction cost over a sequence of linear systems that arise from non‐linear solutions in a plastic regime. Copyright © 2007 John Wiley & Sons, Ltd.     

Sensitivity analysis and shape optimization for preform design in thermo‐mechanical coupled analysis

In complex forging processes, it is essential to find the optimal deformation path and the optimal preform shape that will lead to the desired final shape and service properties. A sensitivity analysis and optimization for preform billet shape in thermo‐mechanical coupled simulation is developed in this work. Non‐linear sensitivity analysis of temperatures, flow‐stresses, strains and strain‐rates are presented with respect to design variables. Both analytical and finite‐difference gradients are employed to validate the effectiveness of sensitivity analysis developed in this work. Numerous iterations of coupled thermo‐mechanical analysis are performed to determine an optimum preform shape based on a given criterion of minimizing the objective function on effective strain variance within the final forging. The design constraints are imposed on die underfill, material scrap, folding defects and temperatures. In addition, a method for material data processing is given in order to determine the flow stress and its derivatives. The shape optimization scheme is demonstrated with the preform designs of an axisymmetric disk and a plane strain problem. Copyright © 1999 John Wiley & Sons, Ltd.     

Computational techniques for optimization of problems involving non‐linear transient simulations

Many optimization problems in engineering require coupling a mathematical programming process to a numerical simulation. When the latter is non‐linear, the resulting computer time may become unaffordably large because three sequential procedures are nested: the outer loop is associated to the optimization process, the middle one corresponds to the time marching scheme and the innermost loop is required for solving iteratively the non‐linear system of equations at each time step. We propose four techniques for reducing CPU time. First, derive the initial values of state variables at each time (innermost loop) from those computed at the previous optimization iteration (outermost loop). Second, select time increment on the basis of those used for the previous optimization iteration. Third, define convergence criteria for the simulation problem on the basis of the optimization process, so that they are only as stringent as really needed. Finally, computations associated to the optimization are shown to be greatly reduced by adopting Newton–Raphson, or a variant, for solving the simulation problem. The effectiveness of these techniques is illustrated through application to three examples involving automatic calibration of non‐linear groundwater flow problems. The total number of iterations is reduced by a factor ranging between 1·7 and 4·6. Copyright © 1999 John Wiley & Sons, Ltd.     

A parallel frontal solver for finite element applications

In finite element simulations, the overall computing time is dominated by the time needed to solve large sparse linear systems of equations. We report on the design and development of a parallel frontal code that can significantly reduce the wallclock time needed for the solution of these systems. The algorithm used is based on dividing the finite element domain into subdomains and applying the frontal method to each subdomain in parallel. The so‐called multiple front approach is shown to reduce the amount of work and memory required compared with the frontal method and, when run on a small number of processes, achieves good speedups. The code, HSL_MP42, has been developed for the Harwell Subroutine Library (http://www.numerical.rl.ac.uk/hsl). It is written in Fortran 90 and, by using MPI for message passing, achieves portability across a wide range of modern computer architectures. Copyright © 2001 John Wiley & Sons, Ltd.     

Improved multi‐level Newton solvers for fully coupled multi‐physics problems

An algorithm is suggested to improve the efficiency of the multi‐level Newton method that is used to solve multi‐physics problems. It accounts for full coupling between the subsystems by using the direct differentiation method rather than error prone finite difference calculations and retains the advantage of greater flexibility over the tightly coupled approaches. Performance of the algorithm is demonstrated by solving a fluid–structure interaction problem. Copyright © 2003 John Wiley & Sons, Ltd.     

Automatic solver for non‐linear partial differential equations with implicit local laws: Application to unilateral contact

In general, non‐linear continuum mechanics combine global balance equations and local constitutive laws. In this work, frictionless contact between a rigid tool and a thin elastic shell is considered. This class of boundary value problems involves two non‐linear algebraic laws: the first one gives explicitly the stress field as a function of the strain throughout the continuum part, whereas the second one is a non‐linear equation relating the contact forces and the displacement at the boundary.Given the fact that classical computational approaches sometimes require significant effort in implementation of complex non‐linear problems, a computation technique based on automatic differentiation of constitutive laws is presented in this paper. The procedure enables to compute automatically the higher‐order derivatives of these constitutive laws and thereafter to define the Taylor series that are the basis of the continuation technique called asymptotic numerical method. The algorithm is about the same with an explicit or implicit constitutive relation. In the modelling of forming processes, many tool shapes can be encountered. The presented computational technique permits an easy implementation of these complex surfaces, for instance in a finite element code: the user is only required to define the tool geometry and the computer is able to obtain the higher‐order derivatives. Copyright © 2013 John Wiley & Sons, Ltd.     

A multi-frontal parallel algorithm for coupled thermo–hydro–mechanical analysis of deforming porous media

In this paper, a multi-frontal parallel algorithm is developed to solve fully coupled heat, water and gas flow in deformable porous media. The mathematical model makes use of the modified effective stress concept together with the capillary pressure relationship and takes phase change and latent heat transfer into account. The chosen macroscopic field variables are displacement, capillary pressure, gas pressure and temperature. The parallel program is developed on a cluster of workstations. The PVM (Parallel Virtual Machine) system is used to handle communications among networked workstations. The multi-frontal method has advantages such as numbering of the finite element mesh in an arbitrary manner, simple programming organization, smaller core requirements and shorter computation times. An implementation of this parallel method on workstations is discussed. The speedup and efficiency of this method is demonstrated and compared with a general domain decomposition method based on band matrix methods by numerical examples. © 1998 John Wiley & Sons, Ltd.     

A semi‐local spectral/hp element solver for linear elasticity problems

We develop an efficient semi‐local method for speeding up the solution of linear systems arising in spectral/hp element discretization of the linear elasticity equations. The main idea is to approximate the element‐wise residual distribution with a localization operator we introduce in this paper, and subsequently solve the local linear system. Additionally, we decouple the three directions of displacement in the localization operator, hence enabling the use of an efficient low energy preconditioner for the conjugate gradient solver. This approach is effective for both nodal and modal bases in the spectral/hp element method, but here, we focus on the modal hierarchical basis. In numerical tests, we verify that there is no loss of accuracy in the semi‐local method, and we obtain good parallel scalability and substantial speed‐up compared to the original formulation. In particular, our tests include both structure‐only and fluid‐structure interaction problems, with the latter modeling a 3D patient‐specific brain aneurysm. Copyright © 2014 John Wiley & Sons, Ltd.     

A new hybrid method for solving linear–non‐linear systems of equations

This paper presents a new method for solving any combination of linear–non‐linear equations. The method is based on the separation of linear equations in terms of some selected variables from the non‐linear ones. The linear group is solved by means of any method suitable for the linear system. This operation needs no iteration. The non‐linear group, however, is solved by an iteration technique based on a new formula using the Taylor series expansion. The method has been described and demonstrated in several examples of analytical systems with very good results. The new method needs the initial approximations for non‐linear variables only. This requires far less computation than the Newton–Raphson method. The method also has a very good convergence rate. The proposed method is most beneficial for engineering systems that very often involve a large number of linear equations with limited number of non‐linear equations. Copyright © 2005 John Wiley & Sons, Ltd.     

An adaptive hybrid time‐stepping scheme for highly non‐linear strongly coupled problems

This paper deals with the design and implementation of an adaptive hybrid scheme for the solution of highly non‐linear, strongly coupled problems. The term ‘hybrid’ refers to a composite time stepping scheme where a controller decides whether a monolithic scheme or a fractional step (splitting) scheme is appropriate for a given time step. The criteria are based on accuracy and efficiency. The key contribution of this paper is the development of a framework for incorporating error criteria for stepsize selection and a mechanism for choosing from splitting or monolithic possibilities. The resulting framework is applied to silylation, a highly non‐linear, strongly coupled problem of solvent diffusion and reaction in deforming polymers. Numerical examples show the efficacy of our new hybrid scheme on both two‐ and three‐dimensional silylation simulations in the context of microlithography. Copyright © 2005 John Wiley & Sons, Ltd.     

Multiscale analysis method for thermo‐mechanical performance of periodic porous materials with interior surface radiation

This study develops a novel multiscale analysis method to predict thermo‐mechanical performance of periodic porous materials with interior surface radiation. In these materials, thermal radiation effect at microscale has an important impact on the macroscopic temperature and stress field, which is our particular interest in this paper. Firstly, the multiscale asymptotic expansions for computing the dynamic thermo‐mechanical coupling problem, which considers the mutual interaction between temperature and displacement field, are given successively. Then, the corresponding numerical algorithm based on the finite element‐difference method is brought forward in details. Finally, some numerical results are presented to verify the validity and relevancy of the proposed method by comparing it with a direct finite element analysis with detailed numerical models. The comparison shows that the new method is effective and valid for predicting the thermo‐mechanical performance and can capture the microstructure behavior of periodic porous materials exactly.s Copyright © 2015 John Wiley & Sons, Ltd.     

A refined non‐linear non‐conforming triangular plate/shell element

A refined non‐conforming triangular plate/shell element for geometric non‐linear analysis of plates/shells using the total Lagrangian/updated Lagrangian approach is constructed in this paper based on the refined non‐conforming element method for geometric non‐linear analysis. The Allman's triangular plane element with vertex degrees of freedom and the refined triangular plate‐bending element RT9 are used to construct the present element. Numerical examples demonstrate that the accuracy of the new element is quite high in the geometric non‐linear analysis of plates/shells. Copyright © 2003 John Wiley & Sons, Ltd.     

A non‐linear programming method approach for upper bound limit analysis

This paper presents a finite element model based on mathematical non‐linear programming in order to determine upper bounds of colapse loads of a mechanical structure. The proposed formulation is derived within a kinematical approach framework, employing two simultaneous and independent field approximations for the velocity and strain rate fields. The augmented Lagrangian is used to establish the compatibility between these two fields. In this model, only continuous velocity fields are used. Uzawa's minimization algorithm is applied to determine the optimal kinematical field that minimizes the difference between external and dissipated work rate. The use of this technique allows to bypass the complexity of the non‐linear aspects of the problem, since non‐linearity is addressed as a set of small local subproblems of optimization for each finite element. The obtained model is quite versatile and suitable for solving a wide range of collapse problems. This paper studies 3D strut‐and‐tie structures, 2D plane strain/stress and 3D solid problems. Copyright © 2007 John Wiley & Sons, Ltd.     

Numerical method for the solution of non‐linear two‐dimensional inverse heat conduction problem using unstructured meshes

A new method of solving multidimensional heat conduction problems is formulated. The developed space marching method allows to determine quickly and exactly unsteady temperature distributions in the construction elements of irregular geometry. The method which is based on temperature measurements at the outer surface, is especially appropriate for determining transient temperature distribution in thick‐wall pressure components. Two examples are included to demonstrate the capabilities of the new approach. Copyright © 2000 John Wiley & Sons, Ltd.     

A general non‐linear optimization algorithm for lower bound limit analysis

The non‐linear programming problem associated with the discrete lower bound limit analysis problem is treated by means of an algorithm where the need to linearize the yield criteria is avoided. The algorithm is an interior point method and is completely general in the sense that no particular finite element discretization or yield criterion is required. As with interior point methods for linear programming the number of iterations is affected only little by the problem size. Some practical implementation issues are discussed with reference to the special structure of the common lower bound load optimization problem, and finally the efficiency and accuracy of the method is demonstrated by means of examples of plate and slab structures obeying different non‐linear yield criteria. Copyright © 2002 John Wiley & Sons, Ltd.     

A face‐based smoothed finite element method (FS‐FEM) for 3D linear and geometrically non‐linear solid mechanics problems using 4‐node tetrahedral elements

This paper presents a novel face‐based smoothed finite element method (FS‐FEM) to improve the accuracy of the finite element method (FEM) for three‐dimensional (3D) problems. The FS‐FEM uses 4‐node tetrahedral elements that can be generated automatically for complicated domains. In the FS‐FEM, the system stiffness matrix is computed using strains smoothed over the smoothing domains associated with the faces of the tetrahedral elements. The results demonstrated that the FS‐FEM is significantly more accurate than the FEM using tetrahedral elements for both linear and geometrically non‐linear solid mechanics problems. In addition, a novel domain‐based selective scheme is proposed leading to a combined FS/NS‐FEM model that is immune from volumetric locking and hence works well for nearly incompressible materials. The implementation of the FS‐FEM is straightforward and no penalty parameters or additional degrees of freedom are used. The computational efficiency of the FS‐FEM is found better than that of the FEM. Copyright © 2008 John Wiley & Sons, Ltd.