Finite Element Solution for Wave Propagation in Layered Fluids

Skull stiffness of children is of great significance to protect brain tissues during traffic accidents. In this paper, the effects of skull stiffness on traumatic brain injury (TBI) are investigated by using a validated 6-year-old child head finite element (FE) model according to Chinese standard GB/T 24550-2009 Results showed that the HIC value, intracranial pressure, Von Mises stress and shear strain of brain tissue increased with the decrease of skull stiffness during the impact of FE model with engine hood. Therefore, the injury risk of the child head decreases with the increase of skull stiffness. And the skull with higher stiffness can provide a better protection for brain tissues during traffic accidents.

There has been a growing demand for nonlinear model updating procedures in the structural dynamics community as advanced vehicles have started to incorporate nonlinearity into their designs. Finite element (FE) model updating is difficult for a nonlinear structure for several reasons: there may be many unknown parameters in the FE model so that multiple solutions may exist, and it is very expensive to compute the structure’s nonlinear normal modes from a full FE model that are an excellent metric to use for nonlinear updating. A recent work showed that some of these challenges can be overcome by updating a nonlinear reduced order model (ROM) rather than the full FE model. The updated ROM can be used to compute response statistics, stresses and ultimately life of the structure. However, one drawback of this approach is that one does not gain physical insight into which parameters in the FE model were in error, and so it is difficult to transfer the lessons learned to future FE models. This work explores the feasibility of updating a FE model to correlate with a ROM with a set of known parameters. The target ROM parameters consist of the linear stiffness and the nonlinear stiffness coefficients which have been identified previously by updating the ROM to correlate with experimental measurements. In this process an optimization routine is setup in which the free parameters are those of the FE model, such as boundary stiffness springs, imperfections, pre-stress, etc. The optimization procedure is wrapped around a ROM creation algorithm that iteratively tunes the FE parameters, creates a ROM, and evaluates the ROM parameters with respect to the target ROM in order to minimize the objective function. This work will demonstrate the procedure on a numerical example of a curved beam in order to verify its effectiveness on the nonlinear model updating.

Background Accurate biomechanical investigation of human intervertebral discs (IVDs) is difficult because of their complicated structural and material features. Aim To investigate probabilistic distributions of the biomechanical responses of the IVD by considering varying nonlinear structural and material properties using a stochastic finite element (FE) model. Methods A FE model of a L3-4 disc was reconstructed, including the nucleus pulposus (NP), annular matrix and fibers. A Monte Carlo method was used to randomly generate 500 sets of the nonlinear material properties and fiber orientations of the disc that were implemented into the FE model. The FE model was analyzed under seven loading conditions: a 500 N compressive force, a 7.5Nm moment simulating flexion, extension, left-right lateral bending, and left-right axial rotation, respectively. The distributions of the ranges of motion (ROMs), intradiscal pressures (IDP), fiber stresses and matrix strains of the disc were analyzed. Results Under the compressive load, the displacement varied between 0.29 mm and 0.76 mm. Under the 7.5Nm moment, the ROMs varied between 3.0° and 6.0° in primary rotations. The IDPs varied within 0.3 MPa under all the loading conditions. The maximal fiber stress (3.22 ± 0.64 MPa) and matrix strain (0.27 ± 0.12%) were observed under the flexion and extension moments, respectively. Conclusion The IVD biomechanics could be dramatically affected by the structural and material parameters used to construct the FE model. The stochastic FE model that includes the probabilistic distributions of the structural and material parameters provides a useful approach to analyze the statistical ranges of the biomechanical responses of the IVDs.

A method for continuous box-girder bridge structure finite element (FE) model updating based on static-load testing is proposed. The procedure includes field static-load testing, FE modeling, FE model (parameter) updating, etc. Based on this procedure, the structure FE model updating for an expressway 5-span pre-stressed concrete continuous box-girder bridge is conducted. And the bridge structure static FE model, which is consistent with the static-load testing actual measure response, is gained. The updated FE model (parameter) is foundation of structural performance evaluation for the bridge.

This paper presents a new adaptive finite element (FE) procedure for accurate, efficient, and reliable computation of the critical buckling loads and the associated modes of nonuniform Bernoulli-Euler members. After the conventional FE solution on a given mesh has been obtained, a novel conceptual and practical strategy is introduced, in which the FE solution of the eigenproblem is equivalently viewed as the FE solution of an associated linear problem. This strategy allows the recently developed element energy projection (EEP) technique to be readily used to calculate super-convergent FE solutions for buckling modes, which are subsequently used to estimate the FE solution errors and to further guide mesh refinements, until the accuracy of the FE solution matches the user-preset error tolerance. Numerical examples are given to show the effectiveness, efficiency, accuracy, and reliability of the proposed method, which also paves the way for development of an adaptive FE solver for more general and complicated eigenproblems.

A reliable and accurate analytical model is desired for the printed circuit board (PCB) with IC package to predict the system response due to loadings such as shock and vibration simulation or even with thermal effect. This work addresses the procedure of model verification by the adoption of experimental modal analysis (EMA) to validate the finite element (FE) model constructed by FE commercial software. The PCB with one package adhered with the heating pad to emulate the heat effect is first considered for completely free boundary condition. The refined FE model of the PCB consists of detail components, such as the chip, substrate, compound and solder balls. The thermal effect on the PCB is simulated to conduct the temperature field analysis as well as the thermal stress. The modal analysis on the PCB with the heating in steady state is then performed to obtain the structural modal parameters, i.e. natural frequencies and mode shapes. The EMA is also carried out to determine the system modal properties that are used to update the analytical FE model. Through the comparison of frequency response functions and modal parameters between the analytical FE model and the real PCB structure, the refined FE model can be verified for material properties and thermal boundary conditions. The same procedure for model verification is then conducted via both EMA and FEA on the PCB in the fixed boundary that complies with the test fixture for the random vibration test of JEDEC specification. The verified equivalent FE model of the PCB can then be adopted to perform spectrum response analysis accordingly.

ABSTRACTObjective: The goal of this study was to explore a framework for developing injury risk functions (IRFs) in a bottom-up approach based on responses of parametrically variable finite element (FE) models representing exemplar populations.Methods: First, a parametric femur modeling tool was developed and validated using a subject-specific (SS)-FE modeling approach. Second, principal component analysis and regression were used to identify parametric geometric descriptors of the human femur and the distribution of those factors for 3 target occupant sizes (5th, 50th, and 95th percentile males). Third, distributions of material parameters of cortical bone were obtained from the literature for 3 target occupant ages (25, 50, and 75 years) using regression analysis. A Monte Carlo method was then implemented to generate populations of FE models of the femur for target occupants, using a parametric femur modeling tool. Simulations were conducted with each of these models under 3-point dynamic bending. Finally, model-based IRFs were developed using logistic regression analysis, based on the moment at fracture observed in the FE simulation. In total, 100 femur FE models incorporating the variation in the population of interest were generated, and 500,000 moments at fracture were observed (applying 5,000 ultimate strains for each synthesized 100 femur FE models) for each target occupant characteristics.Results: Using the proposed framework on this study, the model-based IRFs for 3 target male occupant sizes (5th, 50th, and 95th percentiles) and ages (25, 50, and 75 years) were developed. The model-based IRF was located in the 95% confidence interval of the test-based IRF for the range of 15 to 70% injury risks. The 95% confidence interval of the developed IRF was almost in line with the mean curve due to a large number of data points.Conclusions: The framework proposed in this study would be beneficial for developing the IRFs in a bottom-up manner, whose range of variabilities is informed by the population-based FE model responses. Specifically, this method mitigates the uncertainties in applying empirical scaling and may improve IRF fidelity when a limited number of experimental specimens are available.

ABSTRACTCahn-Hilliard type of phase-field (PF) model coupled with elasticity equations is used to study the instabilities in multilayer thin films. The governing equations of the solid state phase transformation include a 4th order partial differential equation representing the evolution of the conserved PF variable (concentration) coupled to 2nd order partial differential equations representing the mechanical equilibrium. A mixed order Galerkin finite element (FE) model is used including C0 interpolation functions for the displacement, and C1 interpolation functions for the concentration. It is shown that quadratic convergence, expected for conforming elements, is achieved from this coupled mixed-order FE model.Using the PF – FE model, first, we studied the effect of compositional strain on the PF interface thickness and the results of simulations are compared with the analytical solutions of an infinite thin film diffusion couple with a flat interface.Morphological instabilities in binary multilayer thin films are investigated. The alloys with and without intermediate phase are considered, as well as the cases with stable and metastable intermediate phase. Maps of transformations in multilayer systems are carried out considering the effects of initial thickness of layers, compositional strain, and growth of a stable/unstable intermediate phase on the instability of the multilayer thin films. It is shown that at some cases phase transformation, intermediate phase nucleation and growth, or deformation of layers due to high compositional strain can lead to the coarsening of the layers which can result in different mechanical and materials behaviors of the original designed multilayer.

In this study, a finite element (FE) model was adopted to simulate the rutting performance of different asphalt mixtures, using commercial general-purpose FE package, ANSYS. The FE model representing the results included two main properties: the viscoelastic properties, which are represented by Poisson’s ratio and the dynamic modulus (E∗), and the plastic properties, which are represented by the time-hardening creep parameters. Data and results generated from the FE model were put in comparison with those obtained from the asphalt pavement analyzer (APA) test, which showed satisfactory level of accuracy in simulating the rutting behavior. In addition to this, statistically analyzed results indicate a proportional correlation between the number of loading cycles and the accuracy of the obtained FE model results. Thus, it is recommended to use a minimum loading cycle of 2000 when analyzing rutting using the FE model.

Modeling of ultra-high performance fiber reinforced concrete columns under eccentric loading

CHAPTER 15 - FINITE ELEMENT APPLICATIONS TO MORE GENERAL FLUID FLOWS

Application of the Johnson-Cook plasticity model in the finite element simulations of the nanoindentation of the cortical bone.

Partial element equivalent circuit (PEEC) is a convenient method for modeling transient behavior of high temperature superconductors (HTS) magnets made of metal-as insulation windings. In HTS coils, especially those made of tapes, screening currents are known to lower the magnetic field, to generate losses, and to contribute to the mechanical stress. Including screening current calculation in PEEC method can be achieved by subdividing the superconducting tape along its width, leading to larger models and much longer computation time. Herein, we propose a finite element (FE) model for screening currents calculation, which can be combined with PEEC model for transport current addition. The FE model is defined as thin shell using formulation with normal component of electric vector potential T as nodal variable, calculated by an iterative procedure. Source term in the FE model is obtained from variation of radial flux density. Critical current densities calculated in the FE model are fed back to the PEEC model at each step of transport current calculation. This work presents in detail the FE model and its coupling with PEEC model. The model is validated by comparison with other 3D FE models and models with axial symmetry. The effect of reducing the size of FE model, by averaging screening currents in adjacent turns, is also presented in this study. Finally, we present simulation results for current ramps and a quench of a double-pancake magnet, obtained by PEEC with and without adding FE screening current model.

Probabilistic finite element predictions of the human lower limb model in total knee replacement

Surface wave propagation effects on buried segmented pipelines