Superelement Technique Research Articles

Superelement simulation of dynamic characteristics of large-size combined systems «Foundation – reinforced concrete structures – metal structures»

The article presents the effectiveness description, verification, approbation and evaluation of the superelement technique for simulation the dynamic characteristics of large-sized combined systems "foundation - reinforced concrete structures - metal structures".

Lightweight design of a crane frame under stress and stiffness constraints using super-element technique

Crane frame is one of the core components of the crane. Important performance indexes for the design of a frame include stiffness, manufacturability, and durability. Simultaneously, lightweight of the frame is also critical for decreasing the consumption of manufacturing and transportation. Crane is a complicated multibody structure, and therefore, using the traditional method to analyze will consume large amounts of computing time, and the accuracy cannot be expected. In order to solve these problems, a novel and effective method, super-element global modal parameterization, is employed in this article. The advantages of using this approach are that the complex models can be reduced, while the important effects are still taken into account. The design procedure consists of three steps: first, the finite element model is used to analyze the original frame. Then, the stiffness and von Mises stress obtained from the analysis are treated as the design constraints in the next topology and thickness optimization. Finally, a validation of the optimum design for durability is performed, and the results show that all the performances satisfy the requirements. The frame structure has a 15.12% reduction in total mass, while the performance is improved compared to the original.

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.

A new finite element approach for the analysis of slewing bearings in wind turbine generators using superelement techniques

Several analytical models have been proposed to estimate the load distribution and the deformation of slewing bearing assemblies in wind turbine generators (WTGs). Even though they are a useful tool for designers as a first approach, most of them assume rigid rings and rigid supporting structures, leading to inaccurate results; even if compliance is considered in some models, only certain boundary conditions can be taken into account, and their complex and diverse nature make often these models inaccurate. For this reason, WTG manufacturers need costly FE analyses to obtain results adapted to the particular geometries and operational conditions of their yaw and pitch bearings assemblies. In this sense, this work presents a superelement-based FE model that significantly reduces the computational cost with a negligible accuracy loss.

Effect of welding seam spacing and relative bar wall thickness of bus framework on joint’s local mechanical property

Now the researches concerning integral bus mainly focused on design and analysis of overall mechanical property of bus body, and paid little attention to characteristic of local structures, such as joint, plug welding hole, and bolt connection point, etc. So there is much blindness on the design of local connecting structure. Since integral bus body structure cancels large section longitudinal beam, and uses framework made by welding small section bars together as principal part to bear the whole load when the vehicle works, there are many joints receiving high load in the body structure, and local stress concentration can not be avoided. Under such circumstances, by adopting beam-shell mixed model based on super element technique, and selecting a joint commonly used by bus sidewall, the rule of the effect of bar joint’s welding seam spacing on joint’s local mechanical property is investigated in this paper, and the investigating results show that joints have minimum stress concentration with welding seam spacing of 8 mm. To learn whether the above rule is affected by relative bar wall thickness, many groups of bars with different relative bar wall thicknesses are studied experimentally, and the experimental results show that the joints local stress levels vary with different relative bar wall thicknesses, but the rule of the effect of bar joint’s welding seam spacing on joint’s local stress level remains the same. The research is significant for local structure design of bus joint in the future.

Bolt–plate contact assemblies with prestress and external loads: Solved with super element technique

In dynamically loaded bolted assemblies fatigue is the designing factor. The primary quantity that controls the fatigue is the part of the external load that is transferred to the bolt, as described by the ratio between transferred load to external load. In an idealized setting this ratio can be expressed by a stiffness ratio between the plate members and the bolt. The ratio of transferred load is, however, highly dependent on the size and position of the external loading.

Pure equilibrium tetrahedral finite elements for global error estimation by dual analysis

AbstractThis study presents a general procedure of creating pure equilibrium tetrahedral finite elements for use under the elastostatic hypothesis. These pure equilibrium elements are of the Fraeijs de Veubeke type and the degree of the polynomial approximation functions of their internal stress field is the parameter generating this new elements family. The spurious kinematic modes (SKM), inherent in the equilibrium approach, are eliminated at the element level by converting each tetrahedron into a super‐element defined as an assembly of four tetrahedral primitive elements. A mathematical discussion on the number of SKM of the primitive elements as well as their elimination by the super‐element technique has been carried out. The development of first and second degree elements is presented here in detail and their efficiency in the frame of global error estimation by dual analysis is emphasized by two numerical applications. The main attribute of the error estimation by dual analysis is that it provides an upper bound on the global discretization error. Copyright © 2009 John Wiley & Sons, Ltd.

Topology optimization of periodic cellular solids based on a superelement method

It is well known that the structural performance of lightweight cellular solids depends greatly on the design of the representative volume element (RVE). In this article, an integrated topology optimization procedure is developed for the global stiffness maximization of 2D periodic and cyclic-symmetry cellular solids. A design variable linking technique and a superelement method are applied to model the structural periodicity and to reduce the computing time. In order to prevent the numerical instabilities associated with checkerboards in the design process, the quadratic perimeter constraint is used. Finally, the topology optimization problem is solved by the dual optimization algorithm. Several numerical examples are used to test the efficiency of the optimization procedure. Results show that the optimal topology of the RVE is not unique. It greatly depends on the size of the RVE. The computing efficiency can be greatly improved by means of the superelement technique. Also, for the optimal solution, the equivalent torsional rigidity has been compared with what is in the literature, to check the structural efficiency of the obtained topology. It has been observed that the current topology solution has the strongest rigidity when the same volume fraction of solid-phase materials is used.

Computation of flexural properties of HA/PLLA composite using a cell model approach

A three-dimensional finite element analysis was conducted to evaluate the feasibility of predicting the flexural properties of hydroxyapatite-reinforced poly-L-lactide acid (HA/PLLA) biocomposite using three different schemes. The scheme 1, originated from a beam analysis, was used to determine the flexural modulus analytically while the scheme 2 and 3 were designed to have different loading and boundary conditions using a finite element cell modeling approach. An empirical approach using Chow’s formula and experimental data were used for comparison with the predicted results. In order to reduce the computational time and save the storage space involved in determining the effect of varying particle volume fractions on the flexural properties of HA/PLLA, a superelement technique was applied. The results using the scheme 3 and the Chow’s formula were found to be in reasonable agreement with experimental results over the range of particle volume fraction. In addition to the Chow’s formula, local stress distribution and the failure processes in HA/PLLA were simulated using the finite element technique.

2105 An Efficient and Accurate Optimization Process with Automatic External Superelement Techniques

2105 An Efficient and Accurate Optimization Process with Automatic External Superelement Techniques

Frequency domain analysis of model order reduction techniques

In this study, some popular model order reduction and superelement techniques are studied in frequency and time domains. Frequency domain identification (FDI) methods are also applied to semidiscrete finite element equations to obtain reduced order models for structural systems. An FDI algorithm that determines the coefficients of the reduced order model by using nonlinear least squares (NLS) method and subspace based identification (SBI) method are applied to a sample problem and the results are compared with component mode synthesis (CMS) and quasi-static mode synthesis (QSM) methods. In literature, phase errors of model order reduction techniques have not been studied; however, it is shown in this paper that phase errors are also important in evaluating the performance of model order reduction techniques. In general, the NLS and SBI methods have better performance than the CMS and QSM methods; however, as the size of problems increases, the NLS method may have convergence problems and the SBI method may yield estimated models having large orders.

A Multilevel Superelement Technique for Damage Analysis

A multilevel superelement technique is applied to model the effects of circular voids on the effective elastic properties of a porous material. A twodimensional representative volume element with a circular void in its center is initially modeled by a superelement. A thin plate of porous material with a macrocircular hole in the center is constructed with this superelement. The finite element computation is then conducted to estimate the effective Young’s modulus, Poisson’s ratio, and the shear modulus of the material using the ABAQUS code for different void sizes. The values of the isotropic damage variables, DE and DG, under various degree of damage are hence determined. These values are compared with those calculated by using a conventional micromechanics damage model. A new isotropic damage model is proposed based on the results of this analysis. To demonstrate the applicability of this damage model, an example case of a notched cylindrical bar under tensile loading is investigated.

Substructuring in the finite-element analysis of sonar transducer arrays

Finite-element (FE) analysis of arrays of sonar transducers becomes costly in memory and computation time for arrays with many elements. This becomes even more severe a problem if the individual transducers have complex structures. However, because in many cases the individual transducer elements are identical, it is possible to treat them as repeated substructures; each substructure may then be viewed as a superelement which is defined by only those nodes which couple into the overall structure of the array. This technique is analogous to the use of Thevenin equivalent sources in the analysis of complex electrical circuits. By the use of this technique it is possible to analyze the electroacoustic performance of larger arrays than hitherto possible within the limitations set by the computer memory. This paper describes this superelement technique and results are presented for a simple two-element transducer array analyzed for its free (unloaded) vibration behavior both by full FE analysis of the complete structure and by the substructuring technique. The results of the two methods are shown to agree very closely, and measurements on an experimental model compare favorably with the theoretical predictions.

Simulation of Fatigue Crack Growth in Welded Structures Using Superelement

In a complicated welded structure, fatigue cracks may initiate at stress-concentrated regions, where locally high stresses occur due to geometrical discontinuity. In order to investigate the structural integrity of ship structures, various aspects of fatigue crack growth must be taken into consideration ; i. e. spectrum of loading, structural redundancy, welding residual stress, stress biaxiality, and noncollinear crack paths. In the present paper a step-by-step finite element simulation method is proposed for fatigue crack propagation, where the structural redundancy is precisely taken into account by the combination of two-dimensional automatic crack propagation system with a fully three-dimensional structural model by using a superelement technique.In the present paper the step-by-step computational crack propagation approach proposed by Sumi, Chen, and Hayashi is extended to include the superelement, which represents the equivalent stiffness matrix and the nodal force vector of a complicated three-dimensional welded structure surrounding the cracking zone. Several connecting methods of the two-dimensional cracked domain with the superelement are discussed in detail. A relatively relaxed connecting method has been proposed by using the generalized inverse matrix of a nodal transformation matrix, where the nodal points of the crack propagating domain and those of the superelement may locate at different points along the interface boundary without loss of solution accuracy. Comparing the present superelement method with the socalled zooming technique using displacement boundary conditions, it has been confirmed that more reliable results are expected by the present method.This method is applied to the simulation of fatigue crack propagation of welded test specimens. We first measured the welding residual stress, some components of which showed a rather high compressive residual stress so that the reduction of effective stress intensity range could be expected. Numerical simulation has been carried out by using the superelement technique in order to idealize the whole welded structures, and the fatigue crack propagation law is modified to take into account the effect of compressive welding residual stress. The simulated crack paths and the fatigue crack propagation lives are in fairly good agreement with the experimental results.

The use of sparse matrix methods in finite-element codes for structural mechanics applications

In this study, sparse matrix methods are considered as linear solvers in finite-element programs for structural mechanics applications. The factorization schemes used, both for the standard global solution technique and for the partial factorization in the superelement technique, are based on sparse matrix technology [George and Liu, Computer Solution of Large Sparse Positive Definite Systems, Prentice-Hall, 1981; Duff and Reid, ACM Trans. Math Software 9, 302–325 (1983); Ashcraft et al., Int. J. Supercomputer Appl. 1, 10–30 (1987); Ashcraft, “A vector implementation of the multifrontal method for large sparse symmetric positive definite linear systems,” ETA-TR-51, Boeing Computer Services, Seattle, 1987], and tailored for use with the finite-element method for structural mechanics problems as described in [Damhaug, “Sparse solution of linear finite-element equations,” Dr Ing. Thesis 1992: 76, The Norwegian Institute of Technology, 1992].

Space Shuttle redesigned solid rocket booster structural dynamic liftoff predictions and correlations

A transient analysis was performed that predicted and correlated the structural static and dynamic behavior of the Space Shuttle redesigned solid-rocket booster (RSRB) during the first redesigned flight, STS-26R, liftoff. A finite element model of the RSRB was analyzed to predict the accelerations, strains, and displacements measured by developmental flight instrumentation that was bonded to the motor during flight. A detailed RSRB finite element model was developed and correlated for use in analyzing the booster behavior during liftoff loading conditions. This finite element model used MSC/NASTRAN superelement techniques to model all components of the RSRB in detail. The accuracy of the assembled RSRB global model was validated by correlation to static fire and other tests performed by Thiokol Corporation. Mode acceleration transient analysis methods were applied to this validated RSRB global model to predict RSRB structural behavior using the actual loading conditions measured during liftoff. Essential information describing the analytical model and techniques used, correlation of the predicted vs measured RSRB behavior, and conclusion are presented in this study.

Comparative study of dynamic analysis techniques in vehicle simulation

Several dynamic analysis techniques are compared with a planar vehicle model. Cartesian formulation, suspension superelement technique, velocity transformation, and recursive formula are compared. The relation between the recursive formula and velocity transformation is investigated. When those techniques are applied to a planar vehicle with two independent suspensions, the efficiency of those methods was compared. The computational efficiency of the recursive formula was higher than those of other methods for the specific planar vehicle example.

Effect of Openings in Ring-Reinforced Shells

The ring-reinforced shell is a primary structure used in the marine and industrial world. Stress and buckling analysis of such structures is generally based on axisymmetric analysis wherein all openings in the shell are neglected. In real life, such structures have a large number of openings often made in a random manner. In order to design an appropriate reinforcement at such an opening, it is necessary to carry out a detailed local stress analysis. Such an analysis can be made either through the use of part models or by superelements which include the entire structure, as well as the local reinforcement. Zoom analysis using the whole model is expensive and requires knowledge of multilevel super element techniques. Analysis using part models is cheaper and can be equally reliable. This paper investigates the effects of openings on the stress distribution in ring-reinforced shells, such as submarines, using a finite element model. The stress concentration factors (SCF's) in areas adjacent to the opening are determined from this analysis. Using these SCF's, modeling rules for utilization of part models are developed and recommended for use.

Thermal and structural analysis of Hermes

After a brief recap of Hermes TPS and structure principles, we present the organization of thermal and structural analysis of the Hermes project, and we describe the way to resolve the problems of connections between calculations performed by the different Hermes partners. We describe in detail the interactions between the general model of TPS, used for global dimensioning of insulation, and refined thermal models giving an accurate temperature map inside details of “hot” and “cold” structures. The organization for structural analysis is based on a finite element general model which supports preliminary design, loads and vibration analyses. Boundary conditions for refined subpart analyses are cut to size, into the general model by a super element technique. This process involves the use by all partners of efficient computer codes, in the field of structural analysis and optimization integrated with CAD; for this Dassault proposes as a reference: the CATIA-ELFINI system.

Finite element programs based on general programming systems

This article describes the advantages and inconveniences with a finite element programming system, i.e. blocks of routines already thoroughly tested, which has to be built together by a programmer to a finite element program. This program may be a tailor-made program to fit a special problem or a general purpose finite element program. The programming system used as an example in this article consists of 1. ∗NORSAM—finite element programming system 2. ∗DASA — pre- and postprocessors 3. ∗ELLIB—element library Together they form a complete set of subroutines from datageneration through the necessary routines for matrix manipulation to presentation of results, including the multilevel superelement technique. Reference to finite element programs applying the programming system concept, is given at the end of the article. Among others, programs for buckling, elasto-plastic analysis of 3-dimensional membranes and solids, nonlinear pipeline problems, acoustic field problems and transient heat conduction in solids are developed. The multilevel superelement technique has been applied in several of these application programs. The concept of the programming system gives undoubtedly a large saving of time and resources and has proved to be more reliable than conventional methods when developing finite element programs.