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This paper suggests a fatigue life calculation method (A fatigue life calculation method is suggested) for rubber components based on the dynamic crack growth considering shear effect. Dynamic tearing tests were carried out, and the crack length was measured using an optical microscope to calculate the dynamic crack growth rate which characterizes and determines the fatigue life. The algorithm was numerically implemented in finite element code, ABAQUS standard, by using the user subroutine and applied to several rubber components. In the finite element analysis, deformation mode of an element was classified into tension and shear, and a weighting factor was multiplied to a strain energy density according to the degree of shear strain. Tension and compression of an elliptic dumbbell specimen was simulated in order to verify the material parameters of the suggested fatigue life prediction equation and to enhance the reliability of the algorithm. Finally, the fatigue life of a vehicle suspension bushing was calculated and compared with test. There were good agreements in the failure location and the magnitude of the fatigue life. [ABSTRACT FROM AUTHOR]

This paper investigates the use of inverse finite-element modeling (IFEM)-based methods for tissue parameter identification using a rolling indentation probe for surgical palpation. An IFEM-based algorithm is proposed for tissue parameter identification through uniaxial indentation. IFEM-based algorithms are also created for locating and identifying the properties of an embedded tumor through rolling indentation of the soft tissue. Two types of parameter identification for the tissue tumor are investigated (1) identifying the stiffness (μ) of a tumor at a known depth and (2) estimating the depth of the tumor (D) with known mechanical properties. The efficiency of proposed methods has been evaluated through silicone and porcine kidney experiments for both uniaxial indentation and rolling indentation. The results show that both of the proposed IFEM methods for uniaxial indentation and rolling indentation have good robustness and can rapidly converge to the correct results. The tissue properties estimated using the developed method are generic and in good agreement with results obtained from standard material tests. The estimation error of μ through uniaxial indentation is below 3 % for both silicone and kidney; the estimation error of μ for the tumor through rolling indentation is 7-9 %. The estimation error of D through rolling indentation is 1-2 mm. [ABSTRACT FROM AUTHOR]

Finite element based formulations for flexible multibody systems are becoming increasingly popular and as the complexity of the configurations to be treated increases, so does the computational cost. It seems natural to investigate the applicability of parallel processing to this type of problems; domain decomposition techniques have been used extensively for this purpose. In this approach, the computational domain is divided into non-overlapping sub-domains, and the continuity of the displacement field across sub-domain boundaries is enforced via the Lagrange multiplier technique. In the finite element literature, this approach is presented as a mathematical algorithm that enables parallel processing. In this paper, the divided system is viewed as a flexible multibody system, and the sub-domains are connected by kinematic constraints. Consequently, all the techniques applicable to the enforcement of constraints in multibody systems become applicable to the present problem. In particular, it is shown that a combination of the localized Lagrange multiplier technique with the augmented Lagrange formulation leads to interesting solution strategies. The proposed algorithm is compared with the well-known FETI approach with regards to convergence and efficiency characteristics. The present algorithm is relatively simple and leads to improved convergence and efficiency characteristics. Finally, implementation on a parallel computer was conducted for the proposed approach. [ABSTRACT FROM AUTHOR]

The mechanical behaviour of a rock mass is described in this paper using a method that combines experimental and numerical techniques. A new discontinuity (joint) constitutive model is proposed based on the non-associative yield law. Constitutive relationships for an anisotropic rock mass are determined by introducing an interaction between sets of discontinuities and the monolith in which they occur. The model is based on the concept that deformation of the monolith and its associated sets of discontinuities are coupled. An experimental investigation of the concrete foundations of the Bogovina Dam on the Crni Timok River in Serbia has been used to verify the presented numerical model. The tests included discontinuity and monolith sample investigations and large-scale field tests. [ABSTRACT FROM AUTHOR]

In this paper an $$hp$$-FEM implementation on Mathematica is discussed. FEM-implementations on higher-level programming platforms are useful for prototyping new algorithms and ideas, but also serve as testing ground for interesting programming techniques. Here, an $$hp$$-adaptive algorithm for eigenproblems, and the use of precomputed data and generation of highly graded $$hp$$-meshes, are examples of the former and latter, respectively. The performance of the code is evaluated in relation to a suite of benchmark problems for the Laplacian and thin solids in elasticity. [ABSTRACT FROM AUTHOR]

In this paper, heat transfer problems with sharp spatial gradients are analyzed using the Generalized Finite Element Method with global-local enrichment functions ( GFEM). With this approach, scale-bridging enrichment functions are generated on the fly, providing specially-tailored enrichment functions for the problem to be analyzed with no a-priori knowledge of the exact solution. In this work, a decomposition of the linear system of equations is formulated for both steady-state and transient heat transfer problems, allowing for a much more computationally efficient analysis of the problems of interest. With this algorithm, only a small portion of the global system of equations, i.e., the hierarchically added enrichments, need to be re-computed for each loading configuration or time-step. Numerical studies confirm that the condensation scheme does not impact the solution quality, while allowing for more computationally efficient simulations when large problems are considered. We also extend the GFEM to allow for the use of hexahedral elements in the global domain, while still using tetrahedral elements in the local domain, to allow for automatic localized mesh refinement without the use of constrained approximations. Simulations are run with the use of linear and quadratic hexahedral and tetrahedral elements in the global domain. Convergence studies indicate that the use of a different partition of unity (PoU) in the global (hexahedral elements) and local (tetrahedral elements) domains does not adversely impact the solution quality. [ABSTRACT FROM AUTHOR]

This paper presents a methodology for an optimal design of interference fit subjected to fatigue loads. Optimization consists in finding a trade-off between mass and competing safety factors at hub and shaft contact zone as well as in shaft fillet. Developing an effective calculation method for fatigue strength of an interference fitted assembly using the finite element method is one of the main steps of the procedure. Meanwhile, coupling the finite elements model of interference fit with an optimization algorithm is not adequate considering the computing time and the significant number of calculations necessary to portrait the assembly behavior. Therefore, a sequential approximate multi-objective optimization algorithm (SAMOO) is presented. The method involves Design Of Experiments (DOE), interpolation with kriging functions, and multi-objective optimization. Preliminary study of parameter variance, and advanced post-processing of multi-objective optimization, provide engineers with valuable information for identifying an optimal design of interference fit assembly using fewer finite element calculations. [ABSTRACT FROM AUTHOR]

The rotational quaternions represent a unique four dimensional parametrization of rotations in the three dimensional Euclidean space. In the present paper they are used as the basic rotational parameters in formulating the finite-element approach of geometrically exact beam-like structures. The classical concept of parameterizing the rotation matrix by the rotational vector is completely abandoned so that the only rotational parameters are the rotational quaternions representing both rotations and rotational strains in the beam. The space discretization based on the collocation method is used and the adjustment of the Newmark time-integration algorithm to the quaternion parameterizations of rotation is presented. [ABSTRACT FROM AUTHOR]

In this paper we present a new approach for solving elastoplastic problems as second order cone complementarity problems (SOCCPs). Specially, two classes of elastoplastic problems, i.e. the J plasticity problems with combined linear kinematic and isotropic hardening laws and the Drucker-Prager plasticity problems with associative or non-associative flow rules, are taken as the examples to illustrate the main idea of our new approach. In the new approach, firstly, the classical elastoplastic constitutive equations are equivalently reformulated as second order cone complementarity conditions. Secondly, by employing the finite element method and treating the nodal displacements and the plasticity multiplier vectors of Gaussian integration points as the unknown variables, we obtain a standard SOCCP formulation for the elastoplasticity analysis, which enables the using of general SOCCP solvers developed in the field of mathematical programming be directly available in the field of computational plasticity. Finally, a semi-smooth Newton algorithm is suggested to solve the obtained SOCCPs. Numerical results of several classical plasticity benchmark problems confirm the effectiveness and robustness of the SOCCP approach. [ABSTRACT FROM AUTHOR]

In this paper, a new shape identification method in the inverse heat conduction problem (IHCP) is applied to detect the location and size of defects in a solid body. Different defects are modeled in a solid body as an elliptical geometry whose parameters are estimated with a proposed inverse algorithm. The inverse algorithm consists of direct, inverse analysis, and gradient-based optimization method. The direct analysis is used a finite-element method in an unstructured grid system to solve the direct heat conduction problem. The inverse analysis is based on recording temperatures data on surface of solid body that calculates the objective function. The employed gradient-based optimization method is constructed using the adjoint, sensitivity, and conjugate gradient method (Powell-Beal's version) that are used to calculate the gradient of objective function, step size, and minimizing the objective function, respectively. The effects of different noisy temperature data, different cavities on some domains, and different type of defects such as poor cure, porosity, and crack are investigated in this work. The results show that this proposed inverse algorithm is more efficient in detection of defects. [ABSTRACT FROM AUTHOR]

This paper studies adaptive finite element methods (AFEMs), based on piecewise linear elements and newest vertex bisection, for solving second order elliptic equations with piecewise constant coefficients on a polygonal domain Ω⊂ℝ. The main contribution is to build algorithms that hold for a general right-hand side f∈ H( Ω). Prior work assumes almost exclusively that f∈ L( Ω). New data indicators based on local H norms are introduced, and then the AFEMs are based on a standard bulk chasing strategy (or Dörfler marking) combined with a procedure that adapts the mesh to reduce these new indicators. An analysis of our AFEM is given which establishes a contraction property and optimal convergence rates N with 0< s≤1/2. In contrast to previous work, it is shown that it is not necessary to assume a compatible decay s<1/2 of the data estimator, but rather that this is automatically guaranteed by the approximability assumptions on the solution by adaptive meshes, without further assumptions on f; the borderline case s=1/2 yields an additional factor log N. Computable surrogates for the data indicators are introduced and shown to also yield optimal convergence rates N with s≤1/2. [ABSTRACT FROM AUTHOR]

Analysis of transverse vibration of the gear found in a high-speed gearbox considered as an annular plate reflecting gear geometry is the subject of this paper. How gear angular velocity affects the deformation of normal modes of transverse vibration of the system under consideration is analysed. Models considered were discretized by the finite elements method. Numerical computations have been performed in the ANSYS environment. The algorithm to identify the proper distorted mode shapes is presented. The Campbell diagram for the system under consideration is elaborated. The problems discussed here can be useful for engineers dealing with dynamics of rotating machine systems. [ABSTRACT FROM AUTHOR]

In this paper, the constitutive relations of the finite element method are constructed and used for solving two- and three-dimensional problems of the asymmetric theory of elasticity. Different variants of finite elements are considered. The numerical experiments are carried out to evaluate the reliability and computational efficiency of the finite element algorithm based on the comparison between the numerical and analytical solutions, numerical estimation of the convergence and checking of the degree of accuracy, to which the natural boundary conditions are satisfied. The obtained solutions to the two- and three-dimensional problems are interpreted from the viewpoint of their applicability to a design of experiments capable of revealing the facts of couple-stress effects in material under elastic deformation and identification of material constants for the asymmetric theory of elasticity. The capabilities of the finite element algorithm to interpret experimental data and estimate the errors occurring in real experiments have been tested by solving several example problems. [ABSTRACT FROM AUTHOR]

In this paper we propose a finite element approach which simulates the mechanical behaviour of beam assemblies that are subject to large deformations and that develop contact-friction interactions. We focus on detecting and modeling contact-friction interactions within the assembly of beams. Contact between beams-or between parts of the same beam in the case of self-contact, is detected from intermediate geometries defined within proximity zones associating close parts of beam axes. The discretization of contact-friction interactions is performed on these intermediate geometries by means of contact elements, constituted of pairs of material particles which are predicted to enter into contact. A 3D finite strain beam model is used to represent the behaviour of each beam. This model describes the kinematics of each beam cross-section using nine degrees of freedom, and is therefore able to represent plane deformations of these cross-sections. Algorithms are proposed to solve the global nonlinear problem using an implicit scheme, under quasi-static assumptions. Simulation results of the tightening and releasing of knots made on monofilament and multifilament yarns are shown as an application. Straight fibers are first twisted together to make a yarn, before suitable conditions are applied to their ends to form and tighten the knot. Tightening forces are finally released to obtain an equilibrium configuration of the knot without external forces. [ABSTRACT FROM AUTHOR]

Constraint preconditioners have proved very efficient for the solution of ill-conditioned finite element (FE) coupled consolidation problems in a sequential computing environment. Their implementation on parallel computers, however, is not straightforward because of their inherent sequentiality. The present paper describes a novel parallel inexact constraint preconditioner (ParICP) for the efficient solution of linear algebraic systems arising from the FE discretization of the coupled poro-elasticity equations. The ParICP implementation is based on the use of the block factorized sparse approximate inverse incomplete Cholesky preconditioner, which is a very recent and effective development for the parallel preconditioning of symmetric positive definite matrices. The ParICP performance is experimented with in real 3D coupled consolidation problems, proving a scalable and efficient implementation of the constraint preconditioning for high-performance computing. ParICP appears to be a very robust algorithm for solving ill-conditioned large-size coupled models in a parallel computing environment. [ABSTRACT FROM AUTHOR]

A simple analytical approximation is proposed in this paper to calculate the crack tip opening displacement under general random variable amplitude loadings. This approximation is based on a modified Dugdale model for cyclic loadings. The discussion is first given under constant amplitude loading and is extended to several simple cases under variable amplitude loadings. Following this, a general algorithm is proposed under general random variable loadings. Numerical examples are verified with finite element simulations. Following this, hardening effect is included by including a hardening correction function. The proposed analytical approximation is very efficient compared to the direct finite element simulation. The solution can be used for detailed fatigue crack growth analysis under random variable amplitude loadings. [ABSTRACT FROM AUTHOR]

A contact algorithm in the context of the combined discrete element (DE) and finite element (FE) method is proposed. The algorithm, which is based on the node-to-surface method used in finite element method, treats each spherical discrete element as a slave node and the surfaces of the finite element domain as the master surfaces. The contact force on the contact interface is processed by using a penalty function method. Afterward, a modification of the combined DE/FE method is proposed. Following that, the corresponding numerical code is implemented into the in-house developed code. To test the accuracy of the proposed algorithm, the impact between two identical bars and the vibration process of a laminated glass plate under impact of elastic sphere are simulated in elastic range. By comparing the results with the analytical solution and/or that calculated by using LS-DYNA, it is found that they agree with each other very well. The accuracy of the algorithm proposed in this paper is proved. [ABSTRACT FROM AUTHOR]

In this paper, three direct search algorithms, i.e. a modified simplex, random direction search and enhanced Powell's methods together with a new localised response surface method are presented and applied to solve die shape optimisation problems for achieving net-shape accuracy in metal forming processes. The main motivation is to develop efficient and easy to implement optimisation algorithms in metal forming simulations which often involve complex tool and workpiece interaction and coupled thermal and mechanical analysis. Three case studies are presented including a simple upsetting, a 2D blade forging and a forward extrusion problem. In all cases, the objective was to achieve net-shape accuracy of the formed parts, one important criterion for precision forming. C+ + programs were developed to implement these algorithms and to automatically integrate optimisation computation and forging simulation. The optimisation results from the three case problems show that direct search based methods especially the modified simplex and the localised response surface methods are computationally efficient and robust for net-shape forging and extrusion optimisation problems. It is also suggested that these methods can be used in more complex forging problems where die shape design and optimisation are essential for achieving net-shape accuracy. [ABSTRACT FROM AUTHOR]

In this paper, we analyze a cascadic multigrid method for semilinear elliptic problems in which the derivative of the semilinear term is Hölder continuous. We first investigate the standard finite element error estimates of this kind of problem. We then solve the corresponding discrete problems using the cascadic multigrid method. We prove that the algorithm has an optimal order of convergence in energy norm and quasi-optimal computational complexity. We also report some numerical results to support the theory. [ABSTRACT FROM AUTHOR]

The aim of this paper is to present an efficient numerical procedure for the theoretical study of bimolecular reactions. It is based on the R matrix variational formalism and the p-version of the finite element method (p-FEM) for expanding the wave function in a finite basis set, and facilitates the development of an efficient algorithm to invert matrices that significantly reduces the computational time in R matrix calculations. We also utilise the self-consistent finite element method to optimise the elements mesh and provide faster convergence of results. We apply our methodology to the study of the collinear H + H process and evaluate its efficiency by comparing our results with several results previously published in the literature. [ABSTRACT FROM AUTHOR]

This paper focuses on studying and adapting modeling techniques using the finite element method to simulate the rigid die compaction of metal powders. First, it presents the implementation of the cap constitutive model into ABAQUS FE software using the closest point projection algorithm. Then, an inverse modeling procedure was proposed to alleviate the problems raised by the interpretation of the experimental tests and to more accurately determine the material parameters. The objective function is formed, based on the discrepancy in density data between the numerical model prediction and the experiment. Minimization of the objective function with respect to the material parameters was performed using an in-house optimization software shell built on a modified Levenberg-Marquardt method. Thus, an integrated simulation module consisting of an inverse optimization method and a finite element method was developed for modeling the powder compaction process as a whole. The simulation and identification module developed was applied to simulate the compaction of some industrial parts. The results reveal that the maximum absolute error between densities is 2.3%. It corresponds to the precision of the experimental method. [ABSTRACT FROM AUTHOR]

It is important to consider the performances of lightweight, stiffness, strength and rollover safety when designing a bus body. In this paper, the finite element (FE) analysis models including strength, stiffness and rollover crashworthiness of a bus body are first built and then validated by physical tests. Based on the FE models, the design of experiment is implemented and multiple surrogate models are created with response surface method and hybrid radial basis function according to the experimental data. After that, a multi-objective optimization problem (MOP) of the bus body is formulated in which the objective is to minimize the weight and maximize the torsional stiffness of the bus body under the constraints of strength and rollover safety. The MOP is solved by employing multi-objective evolutionary algorithms to obtain the Pareto optimal set. Finally, an optimal solution of the set is chosen as the final design and compared with the original design. [ABSTRACT FROM AUTHOR]

In this paper, an implicit coupling algorithm for fluid-structure interaction problems with under-time steps for the solid is presented. Its implementation on two configurations is achieved by using the CASTEM finite-elements code. First, the free oscillations of a cylinder in an annular fluid domain where its movement is determined by the coupled fluid-solid action is considered in the case of viscous fluid. It should be noted that the implicit coupling algorithm gives the best prediction of the structure oscillations. The under-time steps for the solid are introduced in order to obtain better results. Then, an application whose final objective is to model a floating barrage is studied. The main goal of this application is to predict the displacements of a ring completely immersed and anchored by a cable to the lower boundary of the fluid domain. The finite-element discretization of the Navier-Stokes equations in the ALE formulation is used [ABSTRACT FROM AUTHOR]

Following the approach developed for rods in Part 1 of this paper (Pimenta et al. in Comput. Mech. 42:715-732, ), this work presents a fully conserving algorithm for the integration of the equations of motion in nonlinear shell dynamics. We begin with a re-parameterization of the rotation field in terms of the so-called Rodrigues rotation vector, allowing for an extremely simple update of the rotational variables within the scheme. The weak form is constructed via non-orthogonal projection, the time-collocation of which ensures exact conservation of momentum and total energy in the absence of external forces. Appealing is the fact that general hyperelastic materials (and not only materials with quadratic potentials) are permitted in a totally consistent way. Spatial discretization is performed using the finite element method and the robust performance of the scheme is demonstrated by means of numerical examples. [ABSTRACT FROM AUTHOR]

technique to extract real modes from the identified complex modes is presented in this paper, which enables the normalized real mode shapes, modal masses, and full or reduced mass and stiffness matrices to be obtained. The theoretical derivation of the method is provided in detail. An 11-DOF vibration system is used to validate the algorithm, and to analyze the effects of the number of modes utilized and measurement DOFs on the extraction results. Finally, the method is used to extract real modes from both experimental modal analysis and operational modal analysis. [ABSTRACT FROM AUTHOR]

In this paper we present an algorithm to refine space-time finite element meshes as needed for the numerical solution of parabolic initial boundary value problems. The approach is based on a decomposition of the space-time cylinder into finite elements, which also allows a rather general and flexible discretization in time. This also includes adaptive finite element meshes which move in time. For the handling of three-dimensional spatial domains, and therefore of a four-dimensional space-time cylinder, we describe a refinement strategy to decompose pentatopes into smaller ones. For the discretization of the initial boundary value problem we use an interior penalty Galerkin approach in space, and an upwind technique in time. A numerical example for the transient heat equation confirms the order of convergence as expected from the theory. First numerical results for the transient Navier-Stokes equations and for an adaptive mesh moving in time underline the applicability and flexibility of the presented approach. [ABSTRACT FROM AUTHOR]

This paper is devoted to the approximate solution of a linear first-order functional differential equation which involves delayed and advanced arguments. We seek a solution x, defined for t ∈ (0, k − 1],( k ∈ IN ), which takes given values on the intervals [ − 1, 0] and ( k − 1, k]. Continuing the work started in previous articles on this subject, we introduce and analyse a computational algorithm based on the finite element method for the solution of this problem which is applicable both in the case of constant and variable coefficients. Numerical results are presented and compared with the results obtained by other methods. [ABSTRACT FROM AUTHOR]

Abrasive waterjet machining (AWJM) is a non-conventional process. The mechanism of material removing in AWJM for ductile materials and existing erosion models are reviewed in this paper. To overcome the difficulties of fluid–solid interaction and extra-large deformation problem using finite element method (FEM), the SPH-coupled FEM modeling for abrasive waterjet machining simulation is presented, in which the abrasive waterjet is modeled by SPH particles and the target material is modeled by FE. The two parts interact through contact algorithm. The creativity of this model is multi-materials SPH particles, which contain abrasive and water and mix together uniformly. To build the model, a randomized algorithm is proposed. The material model for the abrasive is first presented. Utilizing this model, abrasive waterjet penetrating the target materials with high velocity is simulated and the mechanism of erosion is depicted. The relationship between the depth of penetration and jet parameters, including water pressure and traverse speed, etc., are analyzed based on the simulation. The results agree with the experimental data well. It will be a benefit to understand the abrasive waterjet cutting mechanism and optimize the operating parameters. [ABSTRACT FROM AUTHOR]

An algorithm combining three-dimensional (3D) discrete and finite element methods is proposed. This new approach is conducted by decomposing the calculation domain into a finite element (FE) calculation domain and a discrete element (DE) calculation domain; the interaction between the two sub-domains is processed by using a penalty function method. Following the established model that combines spherical DEs and FEs, the corresponding numerical code is developed. The vibration process of two cantilever beams under dynamic force is simulated. By comparing the results calculated with different penalty factors set and also with that calculated by the finite element code LS-DYNA, it is found that the calculated results are unanimous and the precision is almost the same as LS-DYNA, as long as the penalty factor is large enough. Moreover, the vibration processes of two plates under impact of rigid spheres are simulated and the accuracy of the model proposed in this paper is further proved in the field of contact mechanics by comparing the simulating results with that calculated by using LS-DYNA. Finally, the impact fracture behavior of a laminated glass plate is simulated, with the influence of model parameters taken into consideration. And the numerical experiments show that the combined model can be used to predict some macroscopical physical quantities, such as the impact force of impactor. [ABSTRACT FROM AUTHOR]

In this paper the application of bees algorithm (BA) in the finite element (FE) model updating of structures is investigated. BA is an optimization algorithm inspired by the natural foraging behavior of honeybees to find food sources. The weighted sum of the squared error between the measured and computed modal parameters is used as the objective function. To demonstrate the effectiveness of the proposed method, BA is applied on a piping system to update several physical parameters of its FE model. To this end, the modal parameters of the numerical model are compared with the experimental ones obtained through modal testing. Moreover, to verify the performance of BA, it is compared with the genetic algorithm, the particle swarm optimization and the inverse eigensensitivity method. Comparison of the results indicates that BA is a simple and robust approach that could be effectively applied to the FE model updating problems. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to propose a size-dependent topology optimization formulation of periodic cellular material microstructures, based on the effective couple-stress continuum model. The present formulation consists of finding the optimal layout of material that minimizes the mean compliance of the macrostructure subject to the constraint of permitted material volume fraction. We determine the effective macroscopic couple-stress constitutive constants by analyzing a unit cell with specified boundary conditions with the representative volume element (RVE) method, based on equivalence of strain energy. The computational model is established by the finite element (FE) method, and the design density and FE stiffness of the RVE are related by the solid isotropic material with penalization power (SIMP) law. The required sensitivity formulation for gradient-based optimization algorithm is also derived. Numerical examples demonstrate that this present formulation can express the size effect during the optimization procedure and provide precise topologies without increase in computational cost. [ABSTRACT FROM AUTHOR]

This paper discusses the problem of structuraloptimization of product families subjected to multiple loadcases, evaluated by computationally costly finite elementanalysis. Product families generally have a complex compositionof shared components that makes individual productoptimization difficult as the relation between the sharedvariables is not always intuitive. More optimal is to treat theproblem as a product family optimization problem. Though,for product families subjected to multiple and computationallycostly crash loads, the optimization problem takestoo long time to solve with traditional methods. Therefore,a new optimization algorithm is presented that decomposesthe family problem into sub-problems and iterativelyreduces the number of sub-problems, decouple and solvethem. The algorithm is applicable for module based productfamilies with predefined composition of generalizedcommonality, subjected to multiple load cases that can beanalyzed separately. The problem reduction is performed byonly considering the constraints that are critical in the optimalsolution. Therefore the optimization algorithm is calledthe Critical Constraint Method, CCM. Finally the CCMalgorithm is evaluated by two product family optimizationproblems. [ABSTRACT FROM AUTHOR]

This paper presents a modified Ant Colony Algorithm(ACA) called multi-city-layer ant colony algorithm(MCLACA). The research attention is focused on improvingthe computational efficiency in the stacking sequenceoptimisation of a laminated composite plate for maximumbuckling load. A new operator, the so-called two point interchange,is introduced and proved to be effective for reducingthe convergence time and enhancing the robustness in theMCLACA performance. The laminate optimisation is subjectto balanced and symmetric layup with ply contiguousand strength constraints. In order to assess the MCLACAperformance, a simply supported rectangular laminate plate,which was taken as numerical example in previous researchusing traditional ACA and genetic algorithm (GA) is chosenas a benchmark case study. Comparing with the ACAand GA results, it is shown that the presented MCLACAhas better performance in terms of computational efficiencyand robustness. To demonstrate the applicability of theMCLACA to a general case, an additional example of laminateoptimisation has been taken with more design variablesand five different boundary conditions by finite elementanalysis. [ABSTRACT FROM AUTHOR]

Abstract  Expression Templates (ET) are a powerful tool for development of user-friendly numerical libraries. By this concept and by operator overloading in C, numerical algorithms can be implemented in a mathematical notation without decreasing the performance in comparison to optimized C or FORTRAN codes. In this paper, we present new Expression Template techniques. First, we explain the concept of “Easy Expression Templates”, which are easier to implement than classical ET. Then, we explain “Fast Expression Templates”. This concept leads to an optimal performance even on special architectures like vector machines. Furthermore, concepts for storing expressions and code optimizing are presented. In order to verify the usability of these programming techniques in real applications, we discuss a template library which calculates local stiffness matrices arising from Finite Element discretizations. [ABSTRACT FROM AUTHOR]

A mortar finite element discretization of the second order elliptic problem in three dimensions, on non-matching grids, using the 3D Crouzeix-Raviart (CR) finite element in each subdomain, is proposed in this paper. The overall discretization is based on using only the nodal values on the mortar side of a subdomain interface for the calculation of the mortar projection, as opposed to applying the conventional approach where some nodal values in the interior of a subdomain are also required. Since the interior degrees of freedom disappear completely from the computation of the mortar projection, the proposed algorithm becomes less intricate and more flexible as compared to the conventional approach. An error estimate is given, and some numerical experiments are presented. [ABSTRACT FROM AUTHOR]

For certain continuum problems, it is desirable and beneficial to combine two different methods together in order to exploit their advantages while evading their disadvantages. In this paper, a bridging transition algorithm is developed for the combination of the meshfree method (MM) with the finite element method (FEM). In this coupled method, the MM is used in the sub-domain where the MM is required to obtain high accuracy, and the FEM is employed in other sub-domains where FEM is required to improve the computational efficiency. The MM domain and the FEM domain are connected by a transition (bridging) region. A modified variational formulation and the Lagrange multiplier method are used to ensure the compatibility of displacements and their gradients. To improve the computational efficiency and reduce the meshing cost in the transition region, regularly distributed transition particles, which are independent of either the meshfree nodes or the FE nodes, can be inserted into the transition region. The newly developed coupled method is applied to the stress analysis of 2D solids and structures in order to investigate its’ performance and study parameters. Numerical results show that the present coupled method is convergent, accurate and stable. The coupled method has a promising potential for practical applications, because it can take advantages of both the MM and FEM when overcome their shortcomings. [ABSTRACT FROM AUTHOR]

Fluid–structure interaction computations based on interface-tracking (moving-mesh) techniques are often hindered if the structural surfaces come in contact with each other. As the distance between two structural surfaces tends to zero, the fluid mesh in between distorts severely and eventually becomes invalid. Our objective is to develop a technique for modeling problems where the contacting structural surfaces would otherwise inhibit flow modeling or even fluid-mesh update. In this paper, we present our contact tracking technique that detects impending contact and maintains a minimum distance between the contacting structural surfaces. Our Surface-Edge-Node Contact Tracking (SENCT) technique conducts a topologically hierarchical search to detect contact between each node and the elements (“surfaces”), edges and other nodes. To keep the contacting surfaces apart by a small distance, we apply to the contacted nodes penalty forces in SENCT-Force (SENCT-F) and displacement restrictions in SENCT-Displacement (SENCT-D). By keeping a minimum distance between the contacting surfaces, we are able to update the fluid mesh in between and model the flow accurately. [ABSTRACT FROM AUTHOR]

A fully conserving algorithm is developed in this paper for the integration of the equations of motion in nonlinear rod dynamics. The starting point is a re-parameterization of the rotation field in terms of the so-called Rodrigues rotation vector, which results in an extremely simple update of the rotational variables. The weak form is constructed with a non-orthogonal projection corresponding to the application of the virtual power theorem. Together with an appropriate time-collocation, it ensures exact conservation of momentum and total energy in the absence of external forces. Appealing is the fact that nonlinear hyperelastic materials (and not only materials with quadratic potentials) are permitted without any prejudice on the conservation properties. Spatial discretization is performed via the finite element method and the performance of the scheme is assessed by means of several numerical simulations. [ABSTRACT FROM AUTHOR]

Generalizing the approach of a previous work of the authors, dealing with two-dimensional (2D) problems, we present multilevel preconditioners for three-dimensional (3D) elliptic problems discretized by a family of Rannacher Turek non-conforming finite elements. Preconditioners based on various multilevel extensions of two-level finite element methods (FEM) lead to iterative methods which often have an optimal order computational complexity with respect to the number of degrees of freedom of the system. Such methods were first presented by Axelsson and Vassilevski in the late-1980s, and are based on (recursive) two-level splittings of the finite element space. An important point to make is that in the case of non-conforming elements the finite element spaces corresponding to two successive levels of mesh refinement are not nested in general. To handle this, a proper two-level basis is required to enable us to fit the general framework for the construction of two-level preconditioners for conforming finite elements and to generalize the method to the multilevel case. In the present paper new estimates of the constant γ in the strengthened Cauchy–Bunyakowski–Schwarz (CBS) inequality are derived that allow an efficient multilevel extension of the related two-level preconditioners. Representative numerical tests well illustrate the optimal complexity of the resulting iterative solver, also for the case of non-smooth coefficients. The second important achievement concerns the experimental study of AMLI solvers applied to the case of micro finite element ( μFEM) simulation. Here the coefficient jumps are resolved on the finest mesh only and therefore the classical CBS inequality based convergence theory is not directly applicable. The obtained results, however, demonstrate the efficiency of the proposed algorithms in this case also, as is illustrated by an example of microstructure analysis of bones. [ABSTRACT FROM AUTHOR]

Imposing rigidity constraints of an immersed elastic body in a transient flow field is not trivial. It requires solution stability and accuracy. In this paper, we present an efficient and accurate algorithm implemented to enforce fluid–structure interface constraints used in the immersed finite element method (IFEM). This interface treatment is a constraint applied onto the rigid bodies based on the fluid structure interaction force evaluated from the immersed solid object. It requires no ad hoc constants or adjustments, thus providing numerical stability and avoiding unnecessary trial-and-error procedures in defining the stiffness of the elastic body. This force term can be evaluated for both uniform and nonuniform fluid grids based on the higher order interpolation function adopted in the IFEM. The ability in handling nonuniform interpolations offers the convenience in modeling arbitrary geometrical shapes and provides solution refinements around interfaces. The results we obtained from flow past a rigid cylinder demonstrate that this convenient way of constraining the interface is a reliable and robust numerical approach to solve unsteady fluid flow interacting with immersed rigid bodies. [ABSTRACT FROM AUTHOR]

Abstract  The paper proposes two scalable variants of the Neumann–Neumann algorithm for the lowest order Crouzeix–Raviart finite element or the nonconforming P 1 finite element on nonmatching meshes. The overall discretization is done using a mortar technique which is based on the application of an approximate matching condition for the discrete functions, requiring function values only at the mesh interface nodes. The algorithms are analyzed using the abstract Schwarz framework, proving a convergence which is independent of the jumps in the coefficients of the problem and only depends logarithmically on the ratio between the subdomain size and the mesh size. [ABSTRACT FROM AUTHOR]

Abstract  The first extension of the virtual fields method to the reconstruction of heterogeneous stiffness properties from 3D bulk full-field displacement data is presented in this paper. Data are provided by Magnetic Resonance Imaging (MRI). Two main issues are addressed: 1. the identification of the stiffness ratio between two different media in a heterogeneous solid; 2. the reconstruction of stiffness heterogeneities buried in a heterogeneous solid. The approach is based on a finite element discretization of the equilibrium equations. It is tested on experimental full-field data obtained on a phantom with the stimulated echo MRI technique. The phantom is made of a stiff spherical inclusion buried within a lower modulus material. Preliminary independent tests showed that the material of the inclusion was four times stiffer than the surrounding material. This ratio value is correctly identified by our approach directly on the phantom with the MRI data. Moreover, the modulus distribution is promisingly reconstructed across the whole investigated volume. However, the resulting modulus distribution is highly variable. This is explained by the fact that the approach relies on a second order differentiation of the data, which tends to amplify noise. Noise is significantly reduced by using appropriate filtering algorithms. [ABSTRACT FROM AUTHOR]

Abstract  This paper deals with the identification of elasto-plastic constitutive parameters from deformation fields measured over the surface of thin flat specimens with the grid method. The approach for recovering the constitutive parameters is the virtual fields method. A dedicated algorithm is used for deriving the distribution of the 2D stress components from the measured deformation fields. A state of plane stress is assumed. Guesses of the constitutive parameters are input in the algorithm and updated until the stresses satisfy the principle of virtual work in the least squares sense. The advantage of this approach is that it can handle very heterogeneous plastic flows and it is much faster than classical finite element model updating approaches. An experimental application is provided to demonstrate it. Six mild steel double-notched specimens have been tested in a configuration combining tension and in-plane bending. The identified parameters are in good agreement with their reference counterparts. Stress fields are eventually reconstructed across the specimen all along the test for analyzing the evolution of the plastic flow. [ABSTRACT FROM AUTHOR]

Abstract  In many problems of geophysical interest, one has to deal with data that exhibit complex fault structures. This occurs, for instance, when describing the topography of seafloor surfaces, mountain ranges, volcanoes, islands, or the shape of geological entities, as well as when dealing with reservoir characterization and modelling. In all these circumstances, due to the presence of large and rapid variations in the data, attempting a fitting using conventional approximation methods necessarily leads to instability phenomena or undesirable oscillations which can locally and even globally hinder the approximation. As will be shown in this paper, the right approach to get a good approximant consists, in effect, in applying first a segmentation process to precisely define the locations of large variations and faults, and exploiting then a discrete approximation technique. To perform the segmentation step, we propose a quasi-automatic algorithm that uses a level set method to obtain from the given (gridded or scattered) Lagrange data several patches delimited by large gradients (or faults). Then, with the knowledge of the location of the discontinuities of the surface, we generate a triangular mesh (which takes into account the identified set of discontinuities) on which a D m -spline approximant is constructed. To show the efficiency of this technique, we will present the results obtained by its application to synthetic datasets as well as real gridded datasets in Oceanography and Geosciences. [ABSTRACT FROM AUTHOR]

Abstract  In this paper, adaptive finite element method is developed for the estimation of distributed parameter in elliptic equation. Both upper and lower error bound are derived and used to improve the accuracy by appropriate mesh refinement. An efficient preconditioned project gradient algorithm is employed to solve the nonlinear least-squares problem arising in the context of parameter identification problem. The efficiency of our error estimators is demonstrated by some numerical experiments. [ABSTRACT FROM AUTHOR]

In this paper a general formulation for finding the maximum allowable dynamic load (MADL) of flexible link mobile manipulators is presented. The main constraints used for the proposed algorithm are the actuator torque capacity and the limited error bound for the end-effector during motion on a given trajectory. The accuracy constraint is taken into account with two boundary lines which are equally offset due to the given end-effector trajectory, while a speed-torque characteristics curve of a typical DC motor is used for applying the actuator torque constraint. The finite element method (FEM), which is able to consider the full nonlinear dynamics of mobile manipulators, is applied to derive the kinematic and dynamic equations. In order to verify the effectiveness of the presented algorithm, two simulation studies considering a flexible two-link planar manipulator mounted on a mobile base are presented and the results are discussed. [ABSTRACT FROM AUTHOR]

In this paper a general formula for finding the maximum allowable dynamic load (MADL) of flexible link mobile manipulators is presented. The main constraints used for the proposed algorithm are the actuator torque capacity and the limited error bound for the end-effector during motion on a given trajectory. The accuracy constraint is taken into account with two boundary lines which are equally offset due to the given end-effector trajectory, while a speed-torque characteristics curve of a typical DC motor, is used for applying the actuator torque constraint. Finite element method (FEM), which is able to consider the full nonlinear dynamic of mobile manipulator is applied to derive the kinematic and dynamic equations. In order to verify the effectiveness of the presented algorithm, two simulation studies considering a flexible two-link planar manipulator mounted on a mobile base are presented and the results are discussed. [ABSTRACT FROM AUTHOR]

This paper presents our new development of parallel finite element algorithms for elastic–plastic problems. The proposed method is based on dividing the original structure under consideration into a number of substructures which are treated as isolated finite element models via the interface conditions. Throughout the analysis, each processor stores only the information relevant to its substructure and generates the local stiffness matrix. A parallel substructure oriented preconditioned conjugate gradient method, which is combined with MR smoothing and diagonal storage scheme are employed to solve linear systems of equations. After having obtained the displacements of the problem under consideration, a substepping scheme is used to integrate elastic–plastic stress–strain relations. The procedure outlined controls the error of the computed stress by choosing each substep size automatically according to a prescribed tolerance. The combination of these algorithms shows a good speedup when increasing the number of processors and the effective solution of 3D elastic–plastic problems whose size is much too large for a single workstation becomes possible. [ABSTRACT FROM AUTHOR]

This paper presents an optimization methodology for non-rigid sheet metal assembly variation by considering part variation, fixture variation, fixture layout, and joint positions, as well as the assembly spring back. The proposed algorithm integrates the finite element analysis (FEA) with a powerful global optimization algorithm, called the mode-pursuing sampling (MPS) method to simultaneously search for the optimal fixture and joint positions in order to minimize the assembly variation. An example application study is presented to demonstrate the optimization procedure and its effectiveness. [ABSTRACT FROM AUTHOR]

This paper presents a new contact searching algorithm for large deformation mortar-based contact formulations. In this algorithm, a bounding volume hierarchy, defined in the context of a binary tree, is built for each contact surface based on the geometry of the surface. A global contact searching procedure based on these bounding volume trees is first performed to find all candidate contact element pairs, and then a local searching procedure is done to find all the mortar segments having contributions to the mortar integrals that define the contact formulation. The searching algorithm is shown to be very efficient and readily applicable to a variety of large sliding contact problems. [ABSTRACT FROM AUTHOR]