Large-scale Finite Element Models Research Articles

Analysis of the Worst Mistuning Patterns in Bladed Disk Assemblies

The problem of determining the worst mistuning patterns is formulated and solved as an optimization problem. Maximum resonant amplitudes searched across the many nodes of a large-scale finite element model of a mistuned bladed disk and across all the excitation frequencies in a given range are combined into an objective function. Individual blade mistuning is controlled by varying design parameters, whose variation range is constrained by manufacture tolerances. Detailed realistic finite element models, which have so far only been used for analyzing tuned bladed disks, are used for calculation of the forced resonant response of mistuned assemblies and for determination of its sensitivity coefficients with respect to mistuning variation. Results of the optimum search of mistuning patterns for some practical bladed disks are analyzed and reveal higher worst cases than those found in previous studies.

Robust control design of active suspensions using modal descriptions of vehicle finite element models

The objective in this paper is to combine the finite element method with the robust control design method. The finite element method results in a high-complexity model with a large number of degrees-of-freedom, which is the basis of the control design. The superposition method is applied as a modal reduction in order to reduce the large-scale finite element model into an acceptable reduced-complexity model. This method guarantees the effective selection of all the significant frequencies in the control design sense. In the design of a robust control, both the performance specification and the model uncertainties are taken into consideration. To demonstrate the effectiveness of the proposed procedure a finite element structure of a bus model with 3444 degrees-of-freedom is applied. The active suspension system designed is tested with the original non-linear finite element model.

Internal ring buckle arrestors for pipe-in-pipe systems

A new buckle arrestor concept for pipe-in-pipe systems is introduced and the results of a systematic study of its performance is presented. The concept involves either one single ring or a number of closely packed narrow rings placed in the annulus between the two pipes. Its effectiveness has been studied through a combination of experiments and analyses. The experiments involved two inch carrier tubes of three different D/ t values and internal rings of various dimensions. A number of experiments were first conducted using pipe-in-pipe systems. It was found that the inner tube had only a small effect on the crossover pressure of this arrestor and, as a result, in many of the following experiments inner tubes were not included. The crossover pressure of the ring arrestors was studied by varying their length, wall thickness and yield stress. Other parameters varied were the dimensions and properties of the two tubes and the gap between the arrestor and the carrier tube. The process resulted in an empirical design formula for the arresting efficiency expressed as a function of the key nondimensional variables of the problem. Large-scale finite element models which simulate the buckle crossover process have also been developed. They have been shown capable of reproducing experiments accurately. Such models can be used to prove an arrestor design developed through the empirical process described in the report.

F-0114 振動低減のための縮退技術を利用した簡便な計算法(S32-1 ファーストオーダーアナリシス(1))(S32 ファーストオーダーアナリシス)

In automotive body structural design, Computer Aided Engineering (CAE) has been widely used in order to evaluate noise, vibration, harshness (NVH). A CAE engineer has usually used a large-scale finite element model exceeding 1 million degrees of freedom to improve NVH performance criteria. It is, however, difficult for a CAE engineer to propose the good modification candidate for the NVH reduction to an automotive designer. Because the FEM calculation is very time-consuming and many design candidates must be considered for a large-scale model. Therefore quick and effective design calculation procedures are requested to overcome these problems, especially in the recent virtual prototyping development process. In this paper, a new optimal design method using a reduction scheme based on the physical coordinates under many design constraints regarding the crashworthiness is proposed in order to overcome above problems. That is, we determine the appropriate location and additional scalar spring constants by minimizing the acceleration of the observation grid. The effectiveness and availability of this method are confirmed using an example.

Shear stress distribution in the trabeculae of human vertebral bone.

The statistical distribution of von Mises stress in the trabeculae of human vertebral cancellous bone was estimated using large-scale finite element models. The goal was to test the hypothesis that average trabecular von Mises stress is correlated to the maximum trabecular level von Mises stress. The hypothesis was proposed to explain the close experimental correlation between apparent strength and stiffness of human cancellous bone tissue. A three-parameter Weibull function described the probability distribution of the estimated von Mises stress (r2>0.99 for each of 23 cases). The mean von Mises stress was linearly related to the standard deviation (r2=0.63) supporting the hypothesis that average and maximum magnitude stress would be correlated. The coefficient of variation (COV) of the von Mises stress was nonlinearly related to apparent compressive strength, apparent stiffness, and bone volume fraction (adjusted r2=0.66, 0.56, 0.54, respectively) by a saturating exponential function [COV = A + B exp(-x/C)]. The COV of the stress was higher for low volume fraction tissue (<0.12) consistent with the weakness of low volume fraction tissue and suggesting that stress variation is better controlled in higher volume fraction tissue. We propose that the average stress and standard deviation of the stress are both controlled by bone remodeling in response to applied loading.

The impact of boundary conditions and mesh size on the accuracy of cancellous bone tissue modulus determination using large-scale finite-element modeling

The apparent properties of cancellous bone are determined by a combination of both hard tissue properties and microstructural organization. A method is desired to extract the underlying hard tissue properties from simple mechanical tests, free from the complications of microstructure. It has been suggested that microCT voxel-based large-scale finite element models could be employed to accomplish this goal (van Rietbergen et al., 1995, Journal of Biomechanics, 28, 69–81). This approach has recently been implemented and it is becoming increasingly popular as finite element models increase in size and sophistication (Fyhrie et al., 1997, Proceedings of the 43rd Annual Meeting of the Orthopaedic Research Society, San Francisco, CA, p. 815; van Rietbergen et al., 1997, Proceedings of the 43rd Annual Meeting of the Orthopaedic Research Society, San Francisco, CA, p. 62). However, no direct quantitative measurements of the accuracy of this method applied to porous structures such as cancellous bone have been made. This project demonstrates the feasibility of this approach by quantifying its best-case accuracy in determining the trabecular hard tissue modulus of analogues fabricated of a material with known material properties determined independently by direct testing. In addition we were able to assess the impact of mesh size and boundary conditions on accuracy. We found that the assumption of a frictionless boundary condition in the parallel plate compression loading configuration was a significant source of error that could be overcome with the use of rigid end-caps similar to those used by Keaveny et al. (1997 Journal of Orthopaedic Research, 15(1), 101–110). In conclusion, we found that this approach is an effective method for determining the average trabecular hard tissue properties of human cancellous bone with an expected practical accuracy level better than 5%.

In-plane biaxial crushing of honeycombs—: Part II: Analysis

The in-plane biaxial crushing experiments on polycarbonate honeycomb presented in Part I are simulated using large scale finite element models. The models account for nonlinearities in geometry and due to contact while the polycarbonate is modeled as an elastic-powerlaw viscoplastic solid. Full-scale simulations of the uniaxial crushing of this honeycomb were shown in the past to reproduce experiments with accuracy. In biaxial crushing, it was not practical to model specimens the same size as those in the experiments due to computational limitations; instead, a smaller model with 10×11 cells was adopted. Results from simulations of seven of the crushing experiments in Part I with various biaxiality ratios are presented. Through parametric studies it is demonstrated that the size of the specimen and friction between the specimen and the loading surfaces affect the initial elastic parts of the stress–displacement responses and the onset of instability. By contrast, for average crushing strains higher than approximately 10%, their effect was relatively small and the calculated responses were in good agreement with the experimental ones. As a consequence, the energy absorption capacity was predicted to good accuracy for all biaxiality ratios. In addition, many of the modes of cell collapse seen in the experiment are reproduced in the simulations.

Flexible multibody dynamic simulation using optimal lumped inertia matrices

A method for dynamic simulation of multibody systems that include large-scale finite element models of flexible bodies is presented. By lumping inertia at a subset of finite element nodes, using an optimal inertia lumping technique, multibody dynamic simulation is performed efficiently and with adequate accuracy. Two numerical examples involving medium and large scale flexible vehicle chassis models are presented to validate the method.

Human vertebral body apparent and hard tissue stiffness

Cancellous bone apparent stiffness and strength are dependent upon material properties at the tissue level and trabecular architecture. Microstructurally accurate, large-scale finite element (LS-FE) models were used to predict the experimental apparent stiffness of human vertebral cancellous bone and to estimate the trabecular hard tissue stiffness. Twenty-eight LS-FE models of cylindrical human vertebral cancellous bone specimens (8 mm in diameter, 9.5 mm in height, one each from twenty-eight individuals) were generated directly from microcomputed tomography images and solved by a special purpose iterative finite element program. The experimental apparent stiffness and strength of the specimens were determined by mechanical testing to failure in the infero–superior direction. Morphometric measurements including bone volume fraction (BV/TV), three eigenvalues of the fabric tensor and average P L were also calculated. The finite element estimate of apparent stiffness explained much of the variance in both experimental apparent stiffness ( r 2=0.89 ) and experimental apparent strength ( r 2=0.87 ). Stepwise linear regression analysis demonstrated that the LS-FE estimated apparent stiffness was the only significant predictor of experimental apparent stiffness and strength when it was included with all measured morphometric values. Hard tissue stiffness was quite variable between individuals (mean, 5.7 GPa; S.D. 1.6 GPa), but was not significantly related to age, sex, race, weight or morphometric measures for this sample.

Nonlinear model reduction strategies for rapid thermal processing systems

We present a systematic method for developing low order nonlinear models from physically based, large scale finite element models of rapid thermal processing (RTP) systems. These low order models are extracted from transient results of a detailed finite element model using the proper orthogonal decomposition (POD) method. Eigenfunctions obtained from the POD method are then used as basis functions in spectral Galerkin expansions of the governing partial differential equations solved by the finite element model to generate the reduced models. Simulation results with the reduced order models demonstrate good agreement with steady state and transient data generated from the finite element model, with an order of magnitude reduction in execution time.

The potential application of finite element modelling of flood plain inundation to predict patterns of overbank deposition

Mathematical modelling of overbank inundation and flows faces many problems and is still in its infancy. Work to date has generally been restricted to small reaches. Large-scale models based on longer reaches of river channel are likely to be of greater value for engineering and flood plain management purposes, but the problems associated with the transition from small to large scales need to be assessed. A large-scale finite element model, RMA-2, has been applied to the flood plain of the lower reaches of the River Culm in southeast Devon, UK. Patterns of radiocaesium accumulation by overbank accretion during flood water inundation were used to assess the potential of using such models for explaining sedimentation rates and patterns. A strong correlation was found between values of the 137Cs inventory and surface concentration and the predicted flood water patterns derived using the RMA-2 model. Except where recession pondage occurs, an inverse relationship existed between 137Cs deposition and water depth. However, the discretization model developed cannot presently cope with large-scale compartmentalization of flows by barriers to flow and small-scale local features, such as ditches crossing the flood plain and the microtopography of the flood plain. This study appraises the potential for using the RMA-2 model to predict patterns of overbank deposition and represents an initial stage in the development of an integrated model of hydraulic and sediment dynamics.

Large-scale contact/impact simulation and sensitivity analysis on distributed-memory computers

A parallel computational strategy is presented for simulating frictional contact/impact response and evaluating sensitivity coefficients for large-scale finite element models of composite structures. The explicit central difference scheme is used for the temporal integration of the semi-discrete governing equations. The two key elements of the strategy are: (a) an element-based domain decomposition technique; and (b) a robust exchange algorithm for communicating information across subdomain interfaces. An implementation of the strategy suitable for any distributed-memory computing system (including clusters of workstations) is described. Numerical results are presented for three structures impacting a rigid surface. The three structures are: an inclined composite cylinder, an inclined stiffened cylinder and an Advanced Composites Technology (ACT) program test panel. For each of these problems, the performance characteristics of the computational procedure are assessed on the IBM SP2 parallel computer system.

Nonlinear Model Reduction Strategies for Rapid Thermal Processing Systems

AbstractThis paper presents a systematic way of developing low order nonlinear models from physically- based, large scale finite element models of rapid thermal processing (RTP) systems. The low order model is extracted from transient results of the finite element model using the proper orthogonal decomposition (POD) method. Eigenfunctions obtained from the POD method are used as basis functions in spectral Galerkin expansions of partial differential equations solved by the finite element model to generate the reduced models. Simulation results demonstrate good agreement with steady state and transient data generated from the finite element model.

An efficient solution method for solving poroelasticity dynamic problems using the finite-element method

Recently, a three-dimensional (3-D) finite-element formulation for the dynamic behavior of poroelastic materials was developed [Panneton etal., J. Acoust. Soc. Am. 96, 3339(A) (1994)]. The fluid and solid macroscopic displacements were used as the fundamental variables. The formulation was based on an analogy with 3-D elastic solid elements. However, six degrees-of-freedom (dof) per node were necessary. For large-scale finite-element models and multifrequency analyses, the use of 6 dof per node has proven to be time- and memory-consuming. Indeed, the complex dissipation mechanisms and frequency-dependent poroelastic coefficients prevent the use of efficient classical solution methods, such as mode superposition method. To alleviate the problem, an efficient solution method is presented. This method is based on assumptions about the poroelastic stress-strain relations and their frequency dependence. A parametric study on the dynamic behavior of poroelastic materials will be presented to back up the used assumptions. Finally, results will be shown to prove that the proposed method leads to substantial gain in computer time without loss of accuracy.

A finite element analysis of the impact-contact problem of a portable telephone using I-DEAS and ADINA

A finite element analysis has been carried out to simulate the phenomenon of a portable telephone that falls and collides with a rigid surface. The new I-DEAS Master Series has been used to create the complicated geometry and finite element mesh for the portable telephone model. The finite element data obtained in I-DEAS is converted to input data for the ADINA system by TRANSOR, an interface program between I-DEAS and ADINA. The large scale finite element model has been solved by the iterative solver on a SUN 4 10 engineering workstation. Interesting results at various stages are: free-fall, impact-contact and, rebound. The possibility of partial breaking of the portable telephone undergoing the impact-contact condition is also discussed.

An algorithm for domain decomposition in finite element analysis

A simple and efficient algorithm is described for automatic decomposition of an arbitrary finite element domain into a specified number of subdomains for finite element and substructuring analysis in a multi-processor computer environment. The algorithm is designed to balance the work loads, to minimize the communication among processors and to minimize the bandwidths of the resulting system of equations. Small- to large-scale finite element models, which have two-node elements (truss, beam element), three-node elements (triangular element) and four-node elements (quadrilateral element), are solved on the Convex computer to illustrate the effectiveness of the proposed algorithm. A FORTRAN computer program is also included.

Stress and free vibration analyses of multilayered composite plates

A two-phase computational procedure is presented for the accurate prediction of the vibration frequencies, stresses and deformations in multilayered composite plates. In the first phase a two-dimensional first-order shear deformation theory is used to predict the global response characteristics (vibration frequencies, ‘average’ through-the-thickness displacements and rotations) as well as the in-plane stress and strain components in the different layers. In the second phase, equilibrium equations and constitutive relations of the three-dimensional theory of elasticity are used to: (1) calculate the transverse stresses and strains as well as the transverse strain energy densities in the different layers; (2) provide better estimates for the composite shear correction factors; and (3) calculate corrected values for the vibration frequencies, displacements, and in-plane strains and stresses. For simply supported plates the predictions of the proposed procedure are shown to be in close agreement with exact three-dimensional elasticity solutions for a wide range of lamination and geometric parameters. Also, the potential of the proposed procedure for use in conjunction with large-scale finite element models of composite structures is discussed.

Vibrational isolation of large scale finite element models using optimization

An optimization system has been developed to minimize the forced vibrational response of large scale finite element models by adjusting isolator elements. The technique can be applied to models under steady state harmonic response and stationary random response. This will automate the design process for vibrational isolation, and the algorithms are expected to solve numerous practical problems.

Efficient reanalysis for structural dynamic response

A technique is presented which will reanalyze the dynamics of a structure due to a limited set of element changes. The method uses a reduced basis of normal modes and efficiently computes the steady state harmonic, stationary random or transient response of a large scale finite element model. The algorithms can be implemented into any general purpose finite element code to save the vibrational analyst both time and money in the design process.