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In this paper, we introduce and analyze multilevel inexact Uzawa and Arrow–Hurwicz algorithms for solving saddle point problems. For the definition of the problem and that of the Uzawa and Arrow–Hurwicz algorithms, we adopt the framework introduced in I. Ekeland and R. Temam, convex analysis and variational problems, North-Holland Publishing Company, Amsterdam, Oxford, 1976, where the saddle point is defined by optimizations on convex sets. The results are obtained for Hilbert spaces, and therefore they can be applied to obtain convergence results for the multigrid methods in finite element spaces. We prove the convergence of the two algorithms, the multilevel Uzawa and the multilevel Arrow–Hurwicz algorithms. Also, we give new convergence proofs for the Uzawa and Arrow–Hurwicz algorithms themselves to better characterize their convergence. [ABSTRACT FROM AUTHOR]

The generalized Schwarz algorithm for a class of elliptic quasi-variational inequalities related to impulse control problems is studied in this paper. The principal result is to prove the error estimate in L ∞ -norm for m subdomains with overlapping nonmatching grids. This approach combines the geometrical convergence and the uniform convergence. [ABSTRACT FROM AUTHOR]

The lattice structures use has increased in several sectors due to the potential for mass reduction without significant rigidity loss. In this paper, an isogrid tube multi-objective optimization considering six objectives is presented. The finite element method was applied to develop a numerical model for this complex structure, and a new optimization algorithm called the Multi-objective Lichtenberg Algorithm was used to find all the best possible designs. The optimizations were made considering two methodologies: (i) using a surrogate model derived from the design of experiments considering the response surface model and (ii) finite element updating, a direct link between the meta-heuristic and the numerical model. The latter is unprecedented in the literature for isogrid tubes and proved to be the best methodology, besides not even needing explicit equations. It discovered isogrid tube designs using TOPSIS that reduced at least 45.69% of the mass, 18.4% of the instability coefficient, 61.76% of the TW, and increased the natural frequency by at least 52.57%. The results show that optimizations via finite element updating associated with meta-heuristics not only allow the true interpretation of complex problems nature through real Pareto fronts, but can also deliver innovative results. [ABSTRACT FROM AUTHOR]

This paper presents a reduced-order finite element (ROFE) method with seldom degrees of freedom for the incompressible miscible displacement problem, where the proper orthogonal decomposition (POD) technique is used. The algorithm process for the ROFE method is provided. Some numerical experiments are presented to help us understand this method and verify the accuracy and efficiency of this method. Meanwhile, numerical results reflect the robustness of the ROFE method in the face of anisotropic and heterogeneous oil reservoir problems. [ABSTRACT FROM AUTHOR]

In this paper, we propose and analyze a second-order decoupled algorithm with different subdomain time steps for the non-stationary Stokes/Darcy model. It is based on the second-order spectral deferred correction method in time and the finite element method in space. We provide the stability and convergence results of our decoupled scheme. Last, some numerical experiments are given to illustrate the accuracy and effectiveness of our decoupled scheme. [ABSTRACT FROM AUTHOR]

In this paper, a second-order hyperbolic equation is solved by a two-grid algorithm combined with the expanded mixed finite element method. The error estimate of the expanded mixed finite element method with discrete-time scheme is demonstrated. Moreover, we present a two-grid method and analyze its convergence. It is shown that the algorithm can achieve asymptotically optimal approximation as long as the mesh sizes satisfy H = O (h 1 2) . Finally, some numerical experiments are provided to illustrate the efficiency and accuracy of the proposed method. [ABSTRACT FROM AUTHOR]

In the ever-expanding fields of thickness and topology optimization, there is a research gap for simultaneous and direct optimization of thickness and material for complex shell structures using fully analytical sensitivities, with prevention of coincident material layers. This paper introduces a novel method to fill this gap: concurrent thickness and material optimization (CTMO) based on a gradient-based approach. This proposed formulation determines optimal thickness and material choice for shell elements within a finite element (FE) model design space. The method of moving asymptotes (MMA) is used for optimization, and material interpolation is handled with solid isotropic material with penalization (SIMP). The behavior of this solver is demonstrated with several academic examples, through a series of extensive parameter sweeps of mass fraction, and minimum and maximum designable thickness, for the compliance minimization objective function. The proposed methodology is geared towards practical design of complex structures, allowing for feasible interpretation into actual engineering solutions. As such, optimization of a small aerobatic aircraft wing is conducted with study of several key design factors. The effects of design restriction and filter size are studied to determine best practices for design procedures. To demonstrate the practical utility of this algorithm, a selected wing optimization result is interpreted into a set of complete, industry style designs, verified through finite element analysis (FEA) to determine deviation from the ideal optimum. It is demonstrated that designs can be interpreted faithfully from optimization results with mass and compliance errors of less than 2%, alongside a discussion of pertinent factors. Finally, several areas with potential for future work are explored. [ABSTRACT FROM AUTHOR]

This paper aims to provide a smart design to improve the efficiency of surface permanent magnet synchronous motor. An efficient design strategy involving penalty approaches are considered for extracting all the possible parameter combinations and the solutions in the infeasible region. We compare the performance of tree heuristic optimization algorithms and six penalty methods. The heuristic optimization algorithms are: particle swarm optimization, differential search algorithm, and tree seed algorithm. The penalty methods are: three of which are static penalty approaches, two of dynamic penalty approaches, and Deb's rule. Besides, the optimized motor design is tested with finite element analysis. Two conclusions were drawn from the experiments. First, heuristic algorithms using penalty approaches had significantly better performance compared to standard and popular heuristic algorithms. This emphasizes the importance of using heuristic algorithms with penalty approaches in SPMSM design optimization. Second, the compatibility of design optimization and numerical analysis results are acceptable and highly satisfactory for surface permanent magnet synchronous motor design. According to the analytical design, a 4% improvement in efficiency was achieved with the proposed approach. [ABSTRACT FROM AUTHOR]

In this paper, we are concerned with the numerical solutions of the coupled fractional Klein-Gordon-Schrödinger equation. The numerical schemes are constructed by combining the Crank-Nicolson/leap-frog difference methods for the temporal discretization and the Galerkin finite element methods for the spatial discretization. We give a detailed analysis of the conservation properties in the senses of discrete mass and energy. Then the numerical solutions are shown to be unconditionally bounded in L2 −norm, H α 2 − semi-norm and L ∞ − norm, respectively. Based on the well-known Brouwer fixed-point theorem and the mathematical induction, the unique solvability of the discrete solutions is proved. Moreover, the schemes are proved to be unconditionally convergent with the optimal order O τ 2 + h r + 1 , where τ is the temporal step, h is the spatial grid size, and r is the order of the selected finite element space. Furthermore, by using the proposed decoupling and iterative algorithms, several numerical examples are included to support theoretical results and show the effectiveness of the schemes. Finally, the fast Krylov subspace solver with suitable circulant preconditioner is designed to effectively solve the Toeplitz-like linear systems. In each iterative step, this method can effectively reduce the memory requirement of above each finite element scheme from O M 2 to O(M), and the computational complexity from O M 3 to O (M log M) , where M is the number of grid nodes. Numerical tests are carried out to show that this fast algorithm is more practical than the traditional backslash and LU factorization/Cholesky decomposition methods, in terms of memory requirement and computational cost. [ABSTRACT FROM AUTHOR]

This paper presents a new isogeometric mortar contact formulation based on an extended finite element interpolation to capture physical pressure discontinuities at the contact boundary. The so called two-half-pass algorithm is employed, which leads to an unbiased formulation and, when applied to the mortar setting, has the additional advantage that the mortar coupling term is no longer present in the contact forces. As a result, the computationally expensive segmentation at overlapping master-slave element boundaries, usually required in mortar methods (although often simplified with loss of accuracy), is not needed from the outset. For the numerical integration of general contact problems, the so-called refined boundary quadrature is employed, which is based on adaptive partitioning of contact elements along the contact boundary. The contact patch test shows that the proposed formulation passes the test without using either segmentation or refined boundary quadrature. Several numerical examples are presented to demonstrate the robustness and accuracy of the proposed formulation. [ABSTRACT FROM AUTHOR]

This paper considers generalized neural elements and identifies the conditions for implementation of functions of algebra of logic from these elements. We introduce the concept of a modified core of Boolean functions with respect to the system of characters of a group on which functions of algebra of logic are given. The criteria of belonging these functions to the class of generalized neurofunctions are provided. The algebraic structure of cores of Boolean neurofunctions is studied. On the basis of properties of tolerance matrices, a number of necessary conditions for implementation of Boolean functions by one generalized neural element are obtained. The obtained results allow to develop efficient methods of synthesis of integer-valued generalized neural elements with a large number of inputs that can be successfully applied in solving information compression and transmission problems, as well as discrete signal recognition problems. [ABSTRACT FROM AUTHOR]

In this paper, a piecewise constant time-stepping discontinuous Galerkin method combined with a piecewise linear finite element method is applied to solve control constrained optimal control problem governed by time fractional diffusion equation. The control variable is approximated by variational discretization approach. The discrete first-order optimality condition is derived based on the first discretize then optimize approach. We demonstrate the commutativity of discretization and optimization for the time-stepping discontinuous Galerkin discretization. Since the state variable and the adjoint state variable in general have weak singularity near t = 0and t = T, a time adaptive algorithm is developed based on step doubling technique, which can be used to guide the time mesh refinement. Numerical examples are given to illustrate the theoretical findings. [ABSTRACT FROM AUTHOR]

Thermal deformation is one of the principal factors that influence the machining accuracy of machine tools, and it can be improved by thermal error compensation. This paper presents a method of thermal error modeling using multisource information fusion, which can further improve the thermal error compensation accuracy. To set up a fusion model with optimal performance, two or more thermal error models should be established, from which a few models should be chosen to complement each other, and then combined into a synthesis model. In this paper, a dynamic thermal error model and a finite element model are combined to build a fusion model for lathe z-direction thermal error according to a fusion algorithm. The inputs for the fusion model are the values detected by the thermal sensors and the infrared imaging. An experiment carried out on a lathe verifies the validity of this modeling method. The results show that the multisource fusion model of thermal error can not only improve the prediction accuracy of thermal error over that of a single model, but also possesses better robustness. [ABSTRACT FROM AUTHOR]

The element energy projection (EEP) method for computation of superconvergent resulting in a one-dimensional finite element method (FEM) is successfully used to self-adaptive FEM analysis of various linear problems, based on which this paper presents a substantial extension of the whole set of technology to nonlinear problems. The main idea behind the technology transfer from linear analysis to nonlinear analysis is to use Newton's method to linearize nonlinear problems into a series of linear problems so that the EEP formulation and the corresponding adaptive strategy can be directly used without the need for specific super-convergence formulation for nonlinear FEM. As a result, a unified and general self-adaptive algorithm for nonlinear FEM analysis is formed. The proposed algorithm is found to be able to produce satisfactory finite element results with accuracy satisfying the user-preset error tolerances by maximum norm anywhere on the mesh. Taking the nonlinear ordinary differential equation of second-order as the model problem, this paper describes the related fundamental idea, the implementation strategy, and the computational algorithm. Representative numerical examples are given to show the efficiency, stability, versatility, and reliability of the proposed approach. [ABSTRACT FROM AUTHOR]

Mesh cleaning is the procedure of removing duplicate nodes, sequencing the indices of remaining nodes, and then updating the mesh connectivity for a topologically invalid Finite Element mesh. To the best of our knowledge, there has been no previously reported work specifically focused on the cleaning of large Finite Element meshes. In this paper we specifically present a generic and straightforward algorithm, MeshCleaner, for cleaning large Finite Element meshes. The presented mesh cleaning algorithm is composed of (1) the stage of compacting and reordering nodes and (2) the stage of updating mesh topology. The basic ideas for performing the above two stages efficiently both in sequential and in parallel are introduced. Furthermore, one serial and two parallel implementations of the algorithm MeshCleaner are developed on multi-core CPU and/or many-core GPU. To evaluate the performance of our algorithm, three groups of experimental tests are conducted. Experimental results indicate that the algorithm MeshCleaner is capable of cleaning large meshes very efficiently, both in sequential and in parallel. The presented mesh cleaning algorithm MeshCleaner is generic, simple, and practical. [ABSTRACT FROM AUTHOR]

Shot peen forming is often used to form the aerodynamic configurations of aircraft integral wing panels. The component is traditionally regarded as perfectly constrained target in peen forming process. However, weak-stiffness of the component results in concomitant macroscopic bending and stretching deformations, and releasing of peening stresses. Subsequent peening stresses are induced by shot impacts based on the current released stresses. In this paper, a intermittently peening-releasing finite element simulation model is used to study peening stress evolution in lowrigidity plate. An algorithm is proposed to calculate the increment of subsequent peening stress by connecting current stresses to the peening stresses in perfectly constrained target.With the algorithm, the peen forming deformations of freely constrained plates are calculated by equivalently simulating the peen forming process. And strip peen forming deformations are calculated and compared with experimental data. The comparison shows the peening deformation of a low-rigidity component should be treated as an incremental process and the algorithm can be used to predict the deformation with good accuracy. [ABSTRACT FROM AUTHOR]

In this paper, a novel energy-preserving numerical scheme for nonlinear Hamiltonian wave equations with Neumann boundary conditions is proposed and analyzed based on the blend of spatial discretization by finite element method (FEM) and time discretization by Average Vector Field (AVF) approach. We first use the finite element discretization in space, which leads to a system of Hamiltonian ODEs whose Hamiltonian can be thought of as the semi-discrete energy of the original continuous system. The stability of the semi-discrete finite element scheme is analyzed. We then apply the AVF approach to the Hamiltonian ODEs to yield a new and efficient fully discrete scheme, which can preserve exactly (machine precision) the semi-discrete energy. The blend of FEM and AVF approach derives a new and efficient numerical scheme for nonlinear Hamiltonian wave equations. The numerical results on a single-soliton problem and a sine-Gordon equation are presented to demonstrate the remarkable energy-preserving property of the proposed numerical scheme. [ABSTRACT FROM AUTHOR]

In this paper, we construct a second order algorithm based on the spectral deferred correction method for the time-dependent magnetohydrodynamics flows at a low magnetic Reynolds number. We present a complete theoretical analysis to prove that this algorithm is unconditionally stable, consistent and second order accuracy. Finally, two numerical examples are given to illustrate the convergence and effectiveness of our algorithm. [ABSTRACT FROM AUTHOR]

A review of the recent development of the machining fixture configuration/layout is presented in this paper. The literature review is mainly focused on the recently developed optimal fixture configuration under the dynamic conditions of the workpiece. In this review paper, the fixture design, fixture analysis, fixture synthesis, fixture layout design, optimization of fixture layout design, various optimization algorithms, and case studies of two- and three-dimensional workpiece geometries under dynamic conditions have been emphasized specially. The further scopes of the research are finally summarized. [ABSTRACT FROM AUTHOR]

Rapid prototyping technology makes the manufacturing of functionally graded material (FGM) objects possible. The FGM production process requires concurrent applications of digital design and manufacturing methods. For this reason, it is imperative to construct and capture information and other critical data regarding the geometry and materials about FGM objects for use in the manufacturing process. This paper proposes a simplex-clear data format for modeling FGM objects. This proposed data format captures both the geometry and material information of an FGM object. It also presents a finite element-based slicing algorithm which slices the FGM object into layers and captures each layer's information for rapid prototyping manufacturing of the object. An example is given at the end of the paper to validate the data format and demonstrate the adaptive slicing algorithm. [ABSTRACT FROM AUTHOR]

The objective of this paper is to introduce an efficient algorithm and implementation for large-scale 3-D topology optimization. The proposed algorithm is an extension of a recently proposed 2-D topological-sensitivity based method that can generate numerous pareto-optimal topologies up to a desired volume fraction, in a single pass. In this paper, we show how the computational challenges in 3-D can be overcome. In particular, we consider an arbitrary 3-D domain-space that is discretized via hexahedral/brick finite elements. Exploiting congruence between elements, we propose a matrix-free implementation of the finite element method. The latter exploits modern multi-core architectures to efficiently solve topology optimization problems involving millions of degrees of freedom. The proposed methodology is illustrated through numerical experiments; comparisons are made against previously published results. [ABSTRACT FROM AUTHOR]

In the present paper, a recent deterministic continuum-strategy two-player discrete-time dynamic leader-follower game with fixed finite time duration and closed-loop information structure is studied. The types of the considered payoff functions can be widely used in different applications (mainly in conflicts of consuming a limited resource, where one player, called the leader, is a superior authority choosing a strategy choice first, and another player, called the follower, chooses after). In case of certain payoff convexity, explicit conditions are given, when it can be known in advance that an equilibrium exists and consists of only two possible choices of both players at each step. The sub-game equilibrium from a given step may depend on the former selections of the players. Thus the continuum-strategy problem has been reduced to a general finite game of two possible choices corresponding to both players. Such type of games could be solved in a standard way with dynamic programming using a computer. Nevertheless, the game can be further simplified, and then an equilibrium can be directly determined, such decreasing the computational demand to a great extent. A solution algorithm and practical examples are also given to support the real-life application of the results. [ABSTRACT FROM AUTHOR]

In the majority of the researches presented so far for behavior analysis of complex structures with random loading and material properties, the applications rather than the analysis algorithms have been extended. The present paper is devoted to extending the probabilistic concepts to achieve a stochastic finite element-based consistent reliability algorithm that is more consistent with the design criteria. The proposed procedure is very general and may be employes for vehcle components with complex geometries and load conditions. However, beam-type vehicle components experience simultaneous spatially-random loading conditions and material properties are employed to clarify the proposed algorithm, without loss of the generality. In this regard, important concepts such as the displacement/stress level-crossing concept are incorporated. The stress stochastic formulations are proposed in the present paper, for the first time. [ABSTRACT FROM AUTHOR]

In this paper, a new type of hybrid finite element method (FEM), hybrid fundamental-solution-based FEM (HFS-FEM), is developed for analyzing plane piezoelectric problems by employing fundamental solutions (Green's functions) as internal interpolation functions. A modified variational functional used in the proposed model is first constructed, and then the assumed intra-element displacement fields satisfying a priori the governing equations of the problem are constructed by using a linear combination of fundamental solutions at a number of source points located outside the element domain. To ensure continuity of fields over inter-element boundaries, conventional shape functions are employed to construct the independent element frame displacement fields defined over the element boundary. The proposed methodology is assessed by several examples with different boundary conditions and is also used to investigate the phenomenon of stress concentration in infinite piezoelectric medium containing a hole under remote loading. The numerical results show that the proposed algorithm has good performance in numerical accuracy and mesh distortion insensitivity compared with analytical solutions and those from ABAQUS. In addition, some new insights on the stress concentration have been clarified and presented in the paper. [ABSTRACT FROM AUTHOR]

Many applications in computational science and engineering concern composite materials, which are characterized by large discontinuities in the material properties. Such applications require fine-scale finite-element meshes, which lead to large linear systems that are challenging to solve with current direct and iterative solutions algorithms. In this paper, we consider the simulation of asphalt concrete, which is a mixture of components with large differences in material stiffness. The discontinuities in material stiffness give rise to many small eigenvalues that negatively affect the convergence of iterative solution algorithms such as the preconditioned conjugate gradient (PCG) method. This paper considers the deflated preconditioned conjugate gradient (DPCG) method in which the rigid body modes of sets of elements with homogeneous material properties are used as deflation vectors. As preconditioner we consider several variants of the algebraic multigrid smoothed aggregation method. We evaluate the performance of the DPCG method on a parallel computer using up to 64 processors. Our test problems are derived from real asphalt core samples, obtained using CT scans. We show that the DPCG method is an efficient and robust technique for solving these challenging linear systems. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new method to analyze the convergence of the standard finite element method for the noncoercive impulse control quasi-variational inequality (QVI). L convergence of the approximation is derived as a result of the geometrical convergence of a Bensoussan-Lions algorithm type and uniform error estimate between the continuous algorithm and its finite element counterpart. This approach is completely different from the one inroduced in [2] as it enables us to derive the error estimate through a computational iterative scheme. [ABSTRACT FROM AUTHOR]

Phononic band gap crystals are made of periodic inclusions embedded in a base material, which can forbid the propagation of elastic and acoustic waves within certain range of frequencies. In the past two decades, the systematic design of phononic band gap crystals has attracted increasing attention due to their wide practical applications such as sound insulation, waveguides, or acoustic wave filtering. This paper proposes a new topology optimization algorithm based on bi-directional evolutionary structural optimization (BESO) method and finite element analysis for the design of phononic band gap crystals. The study on the maximizing gap size between two adjacent bands has been systematically conducted for out-of-plane waves, in-plane waves and the coupled in-plane and out-of-plane waves. Numerical results demonstrate that the proposed optimization algorithm is effective and efficient for the design of phononic band gap crystals and various topological patterns of optimized phononic structures are presented. Several new patterns for phononic band gap crystals have been successfully obtained. [ABSTRACT FROM AUTHOR]

The immersed finite element method (IFEM) is a novel numerical approach to solve fluid-structure interaction types of problems that utilizes non-conforming meshing concept. The fluid and the solid domains are represented independently. The original algorithm of the IFEM follows the interpolation process as illustrated in the original immersed boundary method where the fluid velocity and the interaction force are explicitly coupled. However, the original approach presents many numerical difficulties when the fluid and solid physical properties have large mismatches, such as when the density difference is large and when the solid is a very stiff material. Both situations will lead to divergent or unstable solutions if not handled properly. In this paper, we develop a semi-implicit formulation of the IFEM algorithm so that several terms of the interfacial forces are implicitly evaluated without going through the force distribution process. Based on the 2-D and 3-D examples that we study in this paper, we show that the semi-implicit approach is robust and is capable of handling these highly discontinuous physical properties quite well without any numerical difficulties. [ABSTRACT FROM AUTHOR]

Finite elements analysis (FEA) is now used routinely to interpret skeletal form in terms of function in both medical and biological applications. To produce accurate predictions from FEA models, it is essential that the loading due to muscle action is applied in a physiologically reasonable manner. However, it is common for muscle forces to be represented as simple force vectors applied at a few nodes on the model's surface. It is certainly rare for any wrapping of the muscles to be considered, and yet wrapping not only alters the directions of muscle forces but also applies an additional compressive load from the muscle belly directly to the underlying bone surface. This paper presents a method of applying muscle wrapping to high-resolution voxel-based finite element (FE) models. Such voxel-based models have a number of advantages over standard (geometry-based) FE models, but the increased resolution with which the load can be distributed over a model's surface is particularly advantageous, reflecting more closely how muscle fibre attachments are distributed. In this paper, the development, application and validation of a muscle wrapping method is illustrated using a simple cylinder. The algorithm: (1) calculates the shortest path over the surface of a bone given the points of origin and ultimate attachment of the muscle fibres; (2) fits a Non-Uniform Rational B-Spline (NURBS) curve from the shortest path and calculates its tangent, normal vectors and curvatures so that normal and tangential components of the muscle force can be calculated and applied along the fibre; and (3) automatically distributes the loads between adjacent fibres to cover the bone surface with a fully distributed muscle force, as is observed in vivo. Finally, we present a practical application of this approach to the wrapping of the temporalis muscle around the cranium of a macaque skull. [ABSTRACT FROM AUTHOR]

We consider an algorithm called FEMWARP for warping triangular and tetrahedral finite element meshes that computes the warping using the finite element method itself. The algorithm takes as input a two- or three-dimensional domain defined by a boundary mesh (segments in one dimension or triangles in two dimensions) that has a volume mesh (triangles in two dimensions or tetrahedra in three dimensions) in its interior. It also takes as input a prescribed movement of the boundary mesh. It computes as output updated positions of the vertices of the volume mesh. The first step of the algorithm is to determine from the initial mesh a set of local weights for each interior vertex that describes each interior vertex in terms of the positions of its neighbors. These weights are computed using a finite element stiffness matrix. After a boundary transformation is applied, a linear system of equations based upon the weights is solved to determine the final positions of the interior vertices. The FEMWARP algorithm has been considered in the previous literature (e.g., in a 2001 paper by Baker). FEMWARP has been successful in computing deformed meshes for certain applications. However, sometimes FEMWARP reverses elements; this is our main concern in this paper. We analyze the causes for this undesirable behavior and propose several techniques to make the method more robust against reversals. The most successful of the proposed methods includes combining FEMWARP with an optimization-based untangler. [ABSTRACT FROM AUTHOR]

The work presented in this paper serves as numerical verification of the analytical model developed in the companion paper for nonlinear dynamic analysis of multi-base seismically isolated structures. To this end, two numerical examples have been analyzed using the computational algorithm incorporated into program 3D-BASIS-ME-MB, developed on the basis of the newly-formulated analytical model. The first example concerns a seven-story model structure that was tested on the earthquake simulator at the University at Buffalo and was also used as a verification example for program SAP2000. The second example concerns a two-tower, multi-story structure with a split-level seismic-isolation system. For purposes of verification, key results produced by 3D-BASIS-ME-MB are compared to experimental results, or results obtained from other structural/finite element programs. In both examples, the analyzed structure is excited under conditions of bearing uplift, thus yielding a case of much interest in verifying the capabilities of the developed analysis tool. [ABSTRACT FROM AUTHOR]

A sub-cycling integration algorithm (or named multi-time-steps integration algorithm), which has been successfully applied to FEM dynamical analysis, was firstly presented by Belytschko et al. (Comput Methods Appl Mech Eng 17/18:259–275, 1979). However, the problem of how to apply this type of algorithm to flexible multi-body dynamics (FMD) problems still lacks investigation up to now. Similar to the region-partitioning method used in FEM, this paper presents a central-difference-based sub-cycling integral method by decomposing the variables of an FMD equation into several groups and adopting different integral step sizes to each group of the variables. Based on the condensed form of an FMD equation, a group of common update formulae and a sub-step update formula, which constitute the sub-cycling together, are established in the paper. Furthermore, an implementation flowchart of the sub-cycling is presented. Stability of the sub-cycling will be analyzed and numerical examples will be performed to verify availability and precision of the sub-cycling in part II of the paper. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to detect damage (stiffness degradation) of laminated composite plates from noisy impact response data. The combined finite element method (FEM) with five degrees of freedom (DOF) and the advanced noise filtering algorithm described in this paper may allow us not only to detect the deteriorated elements but also to find their locations and the extents. A first order shear deformation theory (FSDT) is used to predict the structural behavior and to detect damage of laminated composite plates. The filtering procedure is designed by means of a wavelet decomposition together with a selection of the measuring points, and the optimization criterion is constructed on an estimate of the probability of detection using genetic algorithms. All these techniques are applied for the first time to composites. The effects of filtered noise associated with the uncertainty of measurements due to the complex nature of composites are considered for different layup sequences, number of layers, and length–thickness ratios. Several numerical results show that the noise filtering system is computationally efficient in identifying stiffness degradation for complex structures such as laminated composites. [ABSTRACT FROM AUTHOR]

Abstract??Investigations on optimization of structures working in high-cycle load conditions were carried out and are presented in this paper. The development of a simple in application optimization algorithm for such structures was the main object of the authors. The work was concentrated on three principle areas: fatigue of material (with special regard to multiaxial criteria of high-cycle fatigue), parametric optimization of structures, and application of the finite element method. The investigations and numerical implementation of several high-cycle criteria were made and the most convenient one for optimization was selected. The main process of fatigue optimization was preceded by the testing of methods of structural optimization and the preparing the tools for improving the efficiency of the optimization algorithm. This stage includes preparation of software tools based on evolutionary algorithms. In addition, the decision variables were preselected through an investigation of the sensitivity of the objective function on small increments of these variables. The work was illustrated by examples of optimization of mechanical structures working in high-cycle load conditions. As observed in the computational examples, the proposed methodology of optimization allowed effectively lowering the mass of the studied structure while maintaining its durability on an established level. The tools and fatigue optimization methodology presented in this paper have universal character and can be applied to any case of a structure subjected to high-cycle loads. [ABSTRACT FROM AUTHOR]

In this paper a three-dimensional Voronoi cell finite element model is developed for analyzing heterogeneous materials containing a dispersion of ellipsoidal inclusions or voids in the matrix. The paper starts with a description of 3D tessellation of a domain with ellipsoidal heterogeneities, to yield a 3D mesh of Voronoi cells containing the heterogeneities. A surface based tessellation algorithm is developed to account for the shape and size of the ellipsoids in point based tessellation methods. The 3D Voronoi cell finite element model, using the assumed stress hybrid formulation, is developed for determining stresses and displacements in a linear elastic material domain. Special stress functions that introduce classical Lamé functions in ellipsoidal coordinates are implemented to enhance solution convergence. Numerical methods for implementation of algorithms and yielding stable solutions are discussed. Numerical examples are conducted with inclusions and voids to demonstrate the effectiveness of the model. [ABSTRACT FROM AUTHOR]

This paper presents an efficient algorithm for structural topology optimization with material and/or geometric nonlinearities using the moving iso-surface threshold (MIST) method. In this algorithm, all finite element analyses (FEA) are conducted for sub-domains with solid and grey elements via removing all void elements, whereas the response function is constructed in the full design domain. This algorithm allows the removed void elements to be involved in design variable update and to reappear in subsequent iterations. As there are solid materials only in the final optimal topology, problems such as 'layering' and 'islanding' caused by void elements in topology optimization for structures considering large deformations are completely eradicated. Challenges such as 'material reappearance' and 'discontinuity' owing to the removal of void elements are resolved. Numerical results for three typical structures and their comparison with those in the literature are presented to validate the present algorithm. [ABSTRACT FROM AUTHOR]

In order to generate efficient tool path with given precision requirements, scallop height should be kept under a given limit, while the tool path should be as short as possible to reduce machining time. Traditional methods generate CC curves one by one, which makes the final tool path far from being globally optimal. This paper presents an optimal tool path generation model for a ball-end tool which strives to globally optimize a tool path with various objectives and constraints. Two scalar functions are constructed over the part surface to represent the path intervals and the feedrate (with directions). Using the finite element method (FEM), the tool path length minimization model and the machining time minimization model are solved numerically. The proposed method is also suitable for tool path generation on mesh surfaces. Simulation results show that the generated tool path can be direction parallel or contour parallel with different boundary conditions. Compared to most of the conventional tool path generation methods, the proposed method is able to generate more effective tool paths due to the global optimization strategy. [ABSTRACT FROM AUTHOR]

In this paper, the investigation of groups with additional finiteness conditions is continued. Criteria of residual finiteness and of almost local solvability of a periodic F* -group are obtained. [ABSTRACT FROM AUTHOR]

This paper is devoted to the structure that describes the construction of finite distributive lattices. From the viewpoint of application, we consider algorithms of construction and enumeration of distributive lattices and partially ordered sets for finite distributive lattices: A formula for finding the maximum anti-chain with respect to nonintersection is given, it is shown that elements of the lattice can be split into pairs according to comparison, the point of the maximum number of elements in the lattices is considered, and the structure of lattice congruence is described. [ABSTRACT FROM AUTHOR]

This paper presents a method to find all intersections between curved lines such as structural line elements and finite element meshes with intentions to generate smaller, non-compatible, line cells (e.g. bar elements) between crossings. The intersection finding algorithm works for two and three-dimensional meshes constituted by linear, quadratic or higher order elements. Using the proposed algorithm, meshes can then be automatically prepared for finite element analyses with techniques for embedding elements within others or analyses that require lines within solids. The application of the method is demonstrated by a number of numerical examples illustrating its capabilities in handling complex geometries, relative speed and convenience. [ABSTRACT FROM AUTHOR]

In this paper, we study inference for chains of variable order under two distinct contamination regimes. Consider a chain of variable memory on a finite alphabet containing zero, at each instant of time an independent coin is flipped and if it turns head a contamination occurs. In the first regime a zero is read independently of the value of the chain. In the second regime, the value of another chain of variable memory is observed instead of the original one. Our results state that the difference between the transition probabilities of the original process and the corresponding ones of the contaminated process may be bounded above uniformly. Moreover, if the contamination probability is small enough, using a version of the Context algorithm we are able to recover the context tree of the original process through a contaminated sample. [ABSTRACT FROM AUTHOR]

Liouville's theorem describes algebraic functions integrable in terms of generalized elementary functions. In many cases, algorithms based on this theorem make it possible to either evaluate an integral or prove that the integral cannot be 'evaluated in finite terms.' The results of the paper do not improve these algorithms but shed light on the arrangement of the 1-forms integrable in finite terms among all 1-forms on an algebraic curve. [ABSTRACT FROM AUTHOR]

Functional dependency (FD) is one of the most analyzed integrity constraints for any data model. In the relational data model, FDs are defined in a natural way: the values of an attribute set Y depend on the values of another attribute set X, that is, 'Y is a function of X'. FDs are well studied and are widely used in normalization theory. XML functional dependencies (XFD) can be defined in different ways and no universally best definition has been proposed. They are defined by very intricate concepts, and they are mostly based upon XML elements described by XML schema languages such as a DTD or an XML Schema definition. The instances of these elements are semi-structured tuples. A semi-structured tuple is an ordered list of (attribute: value) pairs. We may think of a tuple as a sentence of a formal language, where the values are the terminal symbols and the attribute names are the nonterminal symbols. In this way, the sequence of the attribute names is the left side of a production rule used to accept the next terminal symbol, that is, the next value of the tuple. So the list of values forms the sentence and the list of attributes forms the dual sentence. In this paper, we introduce the notion of the extended tuple as a sentence from a regular language generated by a grammar where the nonterminal symbols of the grammar are the attribute names of the tuple. Sets of extended tuples are the extended relations (relations are instances). We then introduce the dual language, which generates the tuple types allowed to occur in extended relations. We define functional dependencies over extended relations. The syntax of functional dependencies will be given on the graph of the finite state automaton accepting the regular language. Using this model, we can also handle extended relations generated by recursive regular expressions. The implication problem of our class of dependencies is decidable and finitely axiomatizable by a version of the Chase algorithm performed on the graph of the associated finite state automaton. [ABSTRACT FROM AUTHOR]

In this paper, we study a two level method based on Newton's iteration for the nonlinear system arising from the Galerkin finite element approximation to the equations of motion described by the Kelvin-Voigt viscoelastic fluid flow model. The two-grid algorithm is based on three steps. In the first step, the nonlinear system is solved on a coarse mesh $\mathcal {T}_{H}$ to obtain an approximate solution u. In the second step, the nonlinear system is linearized around u based on Newton's iteration and the linear system is solved on a finer mesh $\mathcal {T}_{h}$. Finally, in the third step, a correction to the results obtained in the second step is achieved by solving a linear problem with a different right hand side on $\mathcal {T}_{h}$. Optimal error estimates in L( L)-norm, when $h=\mathcal {O} (H^{2-\delta })$ and in L()-norm, when $h=\mathcal {O}(H^{5-2\delta })$ for velocity and in L( L)-norm, when $h=\mathcal {O}(H^{5-2\delta })$ for pressure are established, where δ > 0 is arbitrarily small for two dimensions and $\delta =\frac {1}{2}$ for three dimensions. [ABSTRACT FROM AUTHOR]

In this paper, a coupled hydro-mechanical formulation is developed for deformable porous media subjected to crack interfaces in the framework of extended finite element method. Governing equations of the porous medium consist of the momentum balance of the bulk together with the momentum balance and continuity equations of the fluid phase, known as [InlineEquation not available: see fulltext.] formulation. The discontinuity in fractured porous medium is modeled for both opening and closing modes that results in the fluid flow within the fracture, and/or contact behavior at the crack edges. The fluid flow through the fracture is assumed to be viscous and is modeled by employing the Darcy law in which the permeability of fracture is obtained using the cubic law. The contact condition in fractured porous medium is handled by taking the advantage from two different algorithms of LATIN method and penalty algorithm. The effect of contact on fluid phase is employed by considering no leak-off from/into the porous medium. The nonlinearity of coupled equations produced due to opening and closing modes is carried out using an iterative algorithm in the Newton-Raphson procedure. Finally, several numerical examples are solved to illustrate the performance of proposed X-FEM method for hydro-mechanical behavior of fractured porous media with opening and closing modes. [ABSTRACT FROM AUTHOR]

This paper presents a composite element algorithm of coupled normal stress and fluid flow process for fractured rock mass, developed from the composite element method (CEM). The coupled relation between the fracture flow and normal stress makes use of the 'filled model', which examines the asperities in the fracture as a layer of granular medium having high porosity and being clipped by the two parallel plates. The existence of fractures is not considered in the mesh generation, but it will be considered explicitly in the mapped composite element. The coupled normal stress and fluid flow process has been simulated by applying a cross iterative algorithm between the two fields. The proposed algorithm considers not only the flow through the fractures, but also the flow exchange between fractures and the surrounding rock blocks. In addition, it can be used for both the filled and non-filled fractures. The verification of the proposed algorithm has been conducted through the illustration of three examples by comparison with the conventional finite element method (FEM), from which the advantages and reliability of the proposed algorithm have been shown clearly. [ABSTRACT FROM AUTHOR]

In the current paper we present a fast, reliable technique for simulating wave propagation in complex structures made of heterogeneous materials. The proposed approach, the spectral cell method, is a combination of the finite cell method and the spectral element method that significantly lowers preprocessing and computational expenditure. The spectral cell method takes advantage of explicit time-integration schemes coupled with a diagonal mass matrix to reduce the time spent on solving the equation system. By employing a fictitious domain approach, this method also helps to eliminate some of the difficulties associated with mesh generation. Besides introducing a proper, specific mass lumping technique, we also study the performance of the low-order and high-order versions of this approach based on several numerical examples. Our results show that the high-order version of the spectral cell method together requires less memory storage and less CPU time than other possible versions, when combined simultaneously with explicit time-integration algorithms. Moreover, as the implementation of the proposed method in available finite element programs is straightforward, these properties turn the method into a viable tool for practical applications such as structural health monitoring [-], quantitative ultrasound applications [], or the active control of vibrations and noise [, ]. [ABSTRACT FROM AUTHOR]

This paper is a follow up of an article published in 2012 by three of the authors, more precisely, of a part of that article dealing with inherently nonfinitely based involutory semigroups. We exhibit a simple condition under which a finite involutory semigroup whose semigroup reduct is inherently nonfinitely based is also inherently nonfinitely based as a unary semigroup. As applications, we get already known as well as new examples of inherently nonfinitely based involutory semigroups. We also show that for finite regular semigroups, our condition is not only sufficient but also necessary for the property of being inherently nonfinitely based to persist. This leads to an algorithmic description of regular inherently nonfinitely based involutory semigroups. [ABSTRACT FROM AUTHOR]

The present paper focuses on the development of a fully implicit, incrementally objective integration algorithm for a hypoelastic formulation of $$J_{2}$$ -viscoplasticity, which employs the mechanical threshold strength model to compute the material's flow stress, taking into account its dependence on strain rate and temperature. Heat generation due to high-rate viscoplastic deformation is accounted for, assuming adiabatic conditions. The implementation of the algorithm is discussed, and its performance is assessed in the contexts of implicit and explicit dynamic finite element analysis, with the aid of example problems involving a wide range of loading rates. Computational results are compared to experimental data, showing very good agreement. [ABSTRACT FROM AUTHOR]

Compressed sensing ensures the accurate reconstruction of sparse signals from far fewer samples than required in the classical Shannon-Nyquist theorem. In this paper, a generalized hard thresholding pursuit (GHTP) algorithm is presented that can recover unknown vectors without the sparsity level information. We also analyze the convergence of the proposed algorithm. Numerical experiments are given for synthetic and real-world data to illustrate the validity and the good performance of the proposed algorithm. [ABSTRACT FROM AUTHOR]