Large Finite Element Models Research Articles

Large-scale stochastic topology optimization using adaptive mesh refinement and coarsening through a two-level parallelization scheme

Topology optimization under uncertainty of large-scale continuum structures is a computational challenge due to the combination of large finite element models and uncertainty propagation methods. The former aims to address the ever-increasing complexity of more and more realistic models, whereas the latter is required to estimate the statistical metrics of the formulation. In this work, the computational burden of the problem is addressed using a sparse grid stochastic collocation method, to calculate the statistical metrics of the topology optimization under uncertainty formulation, and a parallel adaptive mesh refinement method, to efficiently solve each of the stochastic collocation nodes. A two-level parallel processing scheme (TOUU-PS2) is proposed to profit from parallel computation on distributed memory systems: the stochastic nodes are distributed through the distributed memory system, and the efficient computation of each stochastic node is performed partitioning the problem using a domain decomposition strategy and solving each subdomain using an adaptive mesh refinement method. A dynamic load-balancing strategy is used to balance the workload between subdomains, and thus increasing the parallel performance by reducing processor idle time. The topology optimization problem is addressed using the topological derivative concept in combination with a level-set method. The performance and scalability of the proposed methodology are evaluated using several numerical benchmarks and real-world applications, showing good performance and scalability up to thousands of processors.

Reduced-order modelling using nonlinear modes and triple nonlinear modal synthesis

This paper introduces a novel reduced-order modelling technique well-suited to the study of nonlinear vibrations in large finite element models. The method combines the concepts of nonlinear complex modes and characteristic constraint modes – or interface modes – to build a fully algebraic reduced-order model easily solved by standard iterative solvers. The performance of the method is appraised on a nonlinear finite element model of bladed disk in the presence of structural mistuning, highlighting the potential of this new technique to deal with current industrial problematics.

Comprehensive group pile settlement formula based on 3D finite element analyses

In the past, formulas for the settlement of group piles considered only a few input parameters and offered only a limited approximation of the actual settlement. Nowadays, however, thanks to the fast-growing performance of personal computers, it is possible to create large 3-dimensional finite element models with a better and more reliable settlement approximation. On the other hand, 3-dimensional finite element methods for piles are not very common in practice since the required procedure is comparatively cumbersome, expensive and needs a bit more expertise. In order to address this issue, a pile settlement formula was developed in the present study based on about 120 finite element model configurations. The group pile settlement formula incorporates the dimensions of a rectangular raft, namely, the diameter, length and spacing of the piles, vertical uniform pressure, soil moduli up to five layers, ultimate pile-soil resistance, pile-tip resistance and elastic modulus of the piles. In addition to this, the average deflection rate of the raft is estimated. The reliability of the finite element model is verified through laboratory-scale group pile tests. The proposed formula is also checked against five well-documented case studies. The formula may help engineers optimize group pile configurations more efficiently by applying the quality of the 3D finite element estimation to practice.

A Small Deformation Thermoporomechanics Finite Element Model and Its Application to Arterial Tissue Fusion

Understanding the impact of thermally and mechanically loading biological tissue to supraphysiological levels is becoming of increasing importance as complex multiphysical tissue-device interactions increase. The ability to conduct accurate, patient specific computer simulations would provide surgeons with valuable insight into the physical processes occurring within the tissue as it is heated or cooled. Several studies have modeled tissue as porous media, yet fully coupled thermoporomechanics (TPM) models are limited. Therefore, this study introduces a small deformation theory of modeling the TPM occurring within biological tissue. Next, the model is used to simulate the mass, momentum, and energy balance occurring within an artery wall when heated by a tissue fusion device and compared to experimental values. Though limited by its small strain assumption, the model predicted final tissue temperature and water content within one standard deviation of experimental data for seven of seven simulations. Additionally, the model showed the ability to predict the final displacement of the tissue to within 15% of experimental results. These results promote potential design of novel medical devices and more accurate simulations allowing for scientists and surgeons to quickly, yet accurately, assess the effects of surgical procedures as well as provide a first step toward a fully coupled large deformation TPM finite element (FE) model.

Toward a quick evaluation of the performance of gravity installed anchors in clay: Penetration and keying

Gravity installed anchors (GIAs) are the most recent generation of anchoring solutions to moor floating facilities for deepwater oil and gas developments. Challenges associated with GIAs include predicting the initial embedment depth and evaluating the keying performance of the anchor. The former involves high soil strain rate due to large anchor penetration velocity, while the later influences the subsequent behavior and pullout capacity of the anchor. With the coupled Eulerian–Lagrangian method, three-dimensional large deformation finite element models are established to investigate the penetration and keying of GIAs in non-homogeneous clay. In the penetration model, a modified Tresca soil model is adopted to allow the effects of soil strain rate and strain softening, and user-defined hydrodynamic drag force and frictional resistance are introduced via concentrated forces. In the keying model, the anchor line effects are incorporated through a chain equation, and the keying, diving and pulling out behaviors of the anchor can all be replicated. Parametric studies are undertaken at first to quantify the effects of various factors on the performance of GIAs, especially on the penetration and keying behaviors. Based on the results of parametric studies, fitted formulae are proposed to give a quick evaluation of the anchor embedment depth after the installation, and the shackle horizontal displacement, shackle embedment loss and anchor inclination at the end of the keying. Comparative studies are also performed to verify the effectiveness of the fitted formulae.

JuliaFEM - open source solver for both industrial and academia usage

The JuliaFEM software library is a framework that allows for the distributed processing of large Finite Element Models across clusters of computers using simple programming models. It is designed to scale up from single servers to thousands of machines, each offering local computation and storage. The basic design principle is: Everything is non-linear. All physics models are non-linear from which the linearizations are made as special cases. This is work in progress. Thus, if you share the vision, contribute and join the community.

Computational framework for model updating of large scale linear and nonlinear finite element models using state of the art evolution strategy

In this work, a computational framework applying-finite element model updating techniques is presented for identifying the linear and nonlinear parts of large scale dynamic systems using vibration measurements of their components. The measurements are taken to be, response time histories and frequency response functions of nonlinear and linear components of the system. Covariance Matrix Adaptation – Evolution Strategy (CMA-ES) a state of the art optimization algorithm was coupled with robust and accurate finite element analysis software in order to effectively produce optimal computational results. The developed framework is applied to a geometrically complex and lightweight experimental bicycle frame with nonlinear suspension fork components. The identification of modal characteristics of the frame (linear part) is based on an experimental investigation of its dynamic response. The modal characteristics are then used to update the finite element model. The nonlinear suspension components are identified using the experimentally obtained response spectra for each of the components tested separately. Single objective structural identification methods without the need of substructuring methods, are used for estimating the parameters (material properties, shell thickness properties and nonlinear properties) of the finite element models, based on minimizing the deviations between the experimental and analytical dynamic characteristics. Finally, the numerical results of the complete system assembly were compared to the experimental results of the equivalent physical structure of the bike.

From homotopy perturbation technique to reduced order model for multiparametric modal analysis of large finite element models

The paper focuses on the definition of a reduced order model for linear modal analysis. The aim is to supply a suitable mathematical alternative tool compatible for multiparametric analysis of large finite element model considering numerous variable parameters, numerous mode shapes and significant levels of variation. The initial full eigenvalue problem is so replaced by a reduced one considering an efficient projection basis. To build it, we propose to combine homotopy transformation and perturbation technique for each parameter direction to define a reduced order model compatible with the design space. Finally, a complete finite element application highlights the capabilities of the proposal in terms of precision and computational time.

Automated static condensation method for local analysis of large finite element models

In this paper, we introduce an efficient new model reduction method, named the automated static condensation method, which is developed for the local analysis of large finite element models. The algebraic multilevel substructuring procedure is modified appropriately, and then applied to the original static condensation method. The retained substructure, which is the local finite element model to be analyzed, is defined, and then the remaining part of the global model is automatically partitioned into many omitted substructures in an algebraic perspective. For an efficient condensation procedure, a substructural tree diagram and substructural sets are established. Using these, the omitted substructures are sequentially condensed into the retained substructure to construct the reduced model. Using several large practical engineering problems, the performance of the proposed method is demonstrated in terms of its solution accuracy and computational efficiency, compared to the original static condensation method and the superelement technique.

Keying behavior of suction embedded plate anchors with flap in clay

Suction embedded plate anchors (SEPLAs) have been applied extensively in deepwater projects due to their high efficiency and low cost. In this paper, a new plasticity model was developed to simulate the keying behavior of SEPLAs. The model was based on three groups of yield envelopes, which considered three different states between the flap and the main plate. Thus, the plasticity model can consider the flap rotation relative to the fluke. The anchor shank was also considered to investigate the three dimensional (3D) effects of the actual SEPLA shape when deriving the yield envelops. A three dimensional large deformation finite element (3D-LDFE) model with flap rotation and shank considered was also set up. Then 3D-LDFE analysis was carried out to verify the plasticity model. The results given by 3D-LDFE analyses agree well with those by plasticity analyses. The effects of the flap on the embedment loss and pullout capacity, and the effects of loading eccentricity and pullout angle on diving behavior are investigated. Optimal padeye offset and pullout angle to drive the anchor diving are proposed.

Generalized Flexibility Method by the Example of Plane Elastoplastic Problem

The structures elastoplastic deformation process can be studied using the finite elements method (FEM). However, to perform reliable, adequate and real calculations of structures, it is necessary to create large finite element models and to use large-scale software systems for their analysis. Thousands or tens of thousands of equations are involved in it. These calculations take much time. Application of the flexibility method developed on the bases of generalized Mohr formula (generalized flexibility method) allows to create numerical algorithms for elastoplastic calculation of framed structures and to obtain adequate results with no significant processor and time consumption. As a result, a number of preparatory operations increases, however, a number of algebraic equations at each step equals to the number of framed structures indetermination only.

A method for performing efficient parametric dynamic analyses in large finite element models undergoing structural modifications

A typical task in an engineering office is to perform parametric analyses in which the response of the structure is studied when some changes are performed. These changes may be needed in the design phase, during manufacturing or even in service. Nowadays many structural analyses employ large and detailed finite element models on which the different scenarios are considered. Parametric analyses in these structures under dynamic loading mean many code executions, require significant computer resources, result in unmanageable files and block expensive licenses of professional programs. There is a need for efficient, simple procedures which allow to perform such analyses in short time, using few resources and, if possible, releasing professional program licenses. We present a new, simple method for accelerating the parametric analyses in large structures under dynamic loading. The procedure has some similarities to model reduction methods, but no condensation is employed; in fact it can be combined with such methods for even larger efficiency gains. The proposal uses the information of the whole system of equations but only processes those nodal degrees of freedom of interest to the analyst. All needed data are easily accessed in any commercial finite element program and the process takes place entirely outside it. Modifications are introduced in a real reduced modal space and the system is re-ortogonalized. The procedure is accurate and allows for nonproportional damping, addition or elimination of stiffness, of mass and of substructures. We show the performance of the method in two study cases. One consists of modifications in the wing model of an unmanned aerial vehicle. The other one consists in the study of solutions to improve the dynamic behavior of a large civil structure.

Effect of surface tension on the adhesion between a rigid flat punch and a semi-infinite neo-Hookean half-space

We study the effect of surface stress on the retraction of a rigid flat circular punch adhering to an incompressible neo-Hookean half space using a large deformation finite element model (FEM). The effect of surface stress is determined by the dimensionless elasto-capillary number, ω=σ/(Ea), where σ is the isotropic solid–air interface surface stress which we shall called surface tension, E is the small strain Young’s modulus and a is the radius of punch. Adhesion of the punch to the half space is characterized by work of adhesion Wad. Within the range of retraction displacement of this work (less or equal to the punch radius), the stiffness of the system is insensitive to retraction displacement and depends only on the elasto-capillary number. In general, surface tension increases the slope of load–displacement curve or the stiffness of the system. For a given work of adhesion, the pull-off force (displacement) increases (decreases) with surface tension. Our results show that the apparent contact angle is not 90 degrees, as predicted by linear elastic theory, but varies from 20 to 180 degrees and is very sensitive to ω when it is near zero. This result can be potentially used to measure solid surface tension.

Large-scale robust topology optimization using multi-GPU systems

Robust topology optimization of continuum structures is an intensive computational task due to the use of uncertainty propagation methods to estimate the statistical metrics within the topology optimization process. Such a computational problem is exacerbated for large finite element (FE) models in terms of memory consumption and processing time. For these reasons, the efficient resolution of robust topology optimization with large models remains an important computational challenge. This work aims to alleviate these computational constraints proposing a well-suited strategy for Graphics Processing Unit (GPU) computing. Such a proposal exploits the multilevel parallelism provided by multi-GPU systems for the parallel execution both within FE models and through uncertainty propagation methods. Task-level parallelism is used to concurrently evaluate the independent simulation models arising from a sparse grid stochastic collocation method. Data-level parallelism with different granularities is then exploited for the efficient resolution of each simulation model and the computation required by the topology optimization process. The resolution of the different calculations of robust topology optimization pipeline using multi-GPU systems are compared to the classically used multi-CPU implementation achieving significant speedups.

Study on LQR control algorithm using superelement model

The conventional linear quadratic regulator (LQR) control algorithm is one of the most popular active control algorithms. One important issue for LQR control algorithm is the reduction of structure’s degrees of freedom (DOF). In this work, an LQR control algorithm with superelement model is intended to solve this issue leading to the fact that LQR control algorithm can be used in large finite element (FE) model for structure. In proposed model, the Craig-Bampton (C-B) method, which is one of the component mode syntheses (CMS), is used to establish superelement modeling to reduce structure’s DOF and applied to LQR control algorithm to calculate Kalman gain matrix and obtain control forces. And then, the control forces are applied to original structure to simulate the responses of structure by vibration control. And some examples are given. The results show the computational efficiency of proposed model using synthesized models is higher than that of the classical method of LQR control when the DOF of structure is large. And the accuracy of proposed model is well. Meanwhile, the results show that the proposed control has more effects of vibration absorption on the ground structures than underground structures.

Validation and updating in a large automotive vibro-acoustic model using a P-box in the frequency domain

In this paper, a model validation framework is proposed and applied to a large vibro-acoustic finite element (FE) model of a passenger car. The framework introduces a p-box approach with an efficie...

Time response of structures with uncertain parameters under stochastic inputs based on coupled polynomial chaos expansion and component mode synthesis methods

ABSTRACTThis article presents a numerical procedure to compute the stochastic dynamic response of large finite element models with uncertain parameters based on polynomial chaos and component mode synthesis methods. Polynomial chaos expansions at higher orders are used to derive the statistical solution of the dynamic response as well as the Monte Carlo simulation procedure. Based on various component mode synthesis methods, the size of the model is reduced. These methods are coupled with polynomial chaos expansion and the explicit mathematical formulations are given. Numerical results illustrating the accuracy and efficiency of the proposed coupled methodological procedures are presented.

An algorithm for solving frequency responses of a system with Rayleigh damping

This paper proposes a fast algorithm for solving frequency responses of a system with Rayleigh damping. The algorithm combines modal superposition with a model order reduction. Only the modes corresponding to a frequency range which is a little bigger than that of interest are used for modal superposition. Complementary part of contribution of computed modes for frequency response is calculated by a model order reduction method. The Ritz vectors resulted from a shifted undamped system is used in the reduction. Their numbers can adaptively be determined by monitoring the Euclidean norms of the relative residuals associated with the function to be evaluated only at the two endpoints of the frequency band of interest. Eigenproblem of the reduced system is then solved to yield the set of orthogonalized Ritz vectors. The final approximate solution can be represented as superposition of computed modes and orthogonalized Ritz vectors. The accuracy, robustness and computational efficiency of the proposed method are highlighted with the solutions of frequency response problems associated with two large finite element models. It is shown that the present method can remarkably reduce the CPU time required by the direct method to frequency response analysis.

Nacre-like materials using a simple doctor blading technique: Fabrication, testing and modeling

The remarkable mechanical performance of biological materials such as bone, nacre, and spider silk stems from their staggered microstructure in which stiff and strong reinforcements are elongated in the direction of loading, separated by softer interfaces, and shifted relative to each other. This structure results in useful combinations of modulus, strength and toughness and therefore is increasingly mimicked in bio-inspired engineering composites. Here, we report the use of a simple and versatile technique based on doctor-blading to fabricate staggered composites of microscopic alumina tablets with high alignment in a chitosan matrix. Tensile tests on these nacre-like materials show that the modulus and strength of the composite films are enhanced by the incorporation of ceramic tablets, but only up to 15vol% after which all properties degrade. This phenomenon, also reported in the past for most of nacre-like materials, composed of micro/nano tablets, obtained from different techniques, has been limiting our ability to produce large volumes of high-performance nacre-like materials. Examination of the structure of the films revealed that at lower tablet concentrations the tablets are well-aligned and well dispersed thorough the volume of the film. At 15vol% and beyond, we observed tablet misalignment and clustering. In order to investigate the impact of these imperfections on material performance we developed large scale finite element models representative of the structure of the composite films. These models show that the mechanical performance significantly degrades with tablet misalignment, and especially at high tablet concentrations. The simulations along with the SEM images therefore quantitatively explain the experimental trends, e.g. the degradation of mechanical properties at high tablet contents.

Adjoint methods of sensitivity analysis for Lyapunov equation

The existing direct sensitivity analysis of optimal structural vibration control based on Lyapunov's second method is computationally expensive when applied to finite element models with a large number of degree-of-freedom and design variables. A new adjoint sensitivity analysis method is proposed in this paper. Using the new method the sensitivity of the performance index, a time integral of a quadratic function of state variables, with respect to all design variables is calculated by solving two Lyapunov matrix equations. In consideration of computational cost reduction, the new adjoint method is further extended to the reduced order model by Guyan method. This makes the method applicable to large finite element models. Two numerical examples demonstrate the accuracy and efficiency of the proposed method.