Using patient specific finite element models to understand the biomechanics of paediatric spinal deformity surgery

Adolescent idiopathic scoliosis (AIS) is a spinal deformity, which may require surgical correction by attaching rods to the patient’s spine using screws inserted into the vertebrae. Complication rates for deformity correction surgery are unacceptably high. Determining an achievable correction without overloading the adjacent spinal tissues or implants requires an understanding of the mechanical interaction between these components. We have developed novel patient specific modelling software to create individualized finite element models (FEM) representing the thoracolumbar spine and ribcage of scoliosis patients. We are using these models to better understand the biomechanics of spinal deformity correction.

Determination of strain-rate-dependent mechanical behavior of living and fixed osteocytes and chondrocytes using atomic force microscopy and inverse finite element analysis

The aim of this paper is to determine the strain-rate-dependent mechanical behavior of living and fixed osteocytes and chondrocytes, in vitro. Firstly, Atomic Force Microscopy (AFM) was used to obtain the force-indentation curves of these single cells at four different strain-rates. These results were then employed in inverse finite element analysis (FEA) using Modified Standard neo-Hookean Solid (MSnHS) idealization of these cells to determine their mechanical properties. In addition, a FEA model with a newly developed spring element was employed to accurately simulate AFM evaluation in this study. We report that both cytoskeleton (CSK) and intracellular fluid govern the strain-rate-dependent mechanical property of living cells whereas intracellular fluid plays a predominant role on fixed cells’ behavior. In addition, through the comparisons, it can be concluded that osteocytes are stiffer than chondrocytes at all strain-rates tested indicating that the cells could be the biomarker of their tissue origin. Finally, we report that MSnHS is able to capture the strain-rate-dependent mechanical behavior of osteocyte and chondrocyte for both living and fixed cells. Therefore, we concluded that the MSnHS is a good model for exploration of mechanical deformation responses of single osteocytes and chondrocytes. This study could open a new avenue for analysis of mechanical behavior of osteocytes and chondrocytes as well as other similar types of cells.

Finite element analysis investigation of response of pumpkin tissue under uniaxial loading

Finite element analysis (FEA) models of uniaxial loading of pumpkin peel and flesh tissues were developed and validated using experimental results. The tensile model was developed for both linear elastic and plastic material models, the compression model was develop d only with the plastic material model. The outcomes of force versus time curves obtained from FEA models followed similar pattern to the experimental curves however the curve resulted with linear elastic material properties had a higher difference with the experimental curves. The values of predicted forces were determined and compared with the experimental curve. An error indicator was introduced and computed for each case and compared. Additionally Root Mean Square Error (RMSE) values were also calculated for each model and compared. The results of modelling were used to develop material model for peel and flesh tissues in FEA modelling of mechanical peeling of tough skinned vegetables.

A Doubly curved Quadrilateral finite-element for the analysis of laminated anisotropic thin shells of revoution

The details of development of the stiffness matrix for a doubly curved quadrilateral element suited for static and dynamic analysis of laminated anisotropic thin shells of revolution are reported. Expressing the assumed displacement state over the middle surface of the shell as products of one-dimensional first order Hermite polynomials, it is possible to ensure that the displacement state for the assembled set of such elements, is geometrically admissible. Monotonic convergence of total potential energy is therefore possible as the modelling is successively refined. Systematic evaluation of performance of the element is conducted, considering various examples for which analytical or other solutions are available.

Material characterisation and numerical modelling of gypsum plasterboards in fire

The fire resistance characteristic of LSF wall systems mainly depends on the protective linings in use, commonly gypsum plasterboards. However, unclassified boards with varying composition and more notably with ambiguous thermal properties are increasingly becoming available in the market. Therefore a study was undertaken with an aim to set minimum standards for fire protective boards used in LSF wall applications. This paper presents the details of this study based on material characterisation and finite element thermal modelling of the most commonly used fire protective board, gypsum plasterboards, to address these critical issues related to fire safety design. In the material characterisation phase of this study, thermal properties of three different gypsum plasterboards manufactured in Australia were measured, analysed and compared. Subsequently, it proposes a thermal property based “k-factor” capable of giving an overall measure of the fire performance of boards, so that it can be used in appropriately classifying fire protective boards. As it is not known how this factor relates to the overall fire performance of LSF wall systems, numerical models were also developed and used to simulate the performance of LSF walls exposed to the standard fire. Finally, a correlation between time-temperature profiles from numerical analyses and calculated k-factors was established.

The partition of unity finite element method for elastic wave propagation in Reissner-Mindlin plates

This paper reports a numerical method for modelling the elastic wave propagation in plates. The method is based on the partition of unity approach, in which the approximate spectral properties of the infinite dimensional system are embedded within the space of a conventional finite element method through a consistent technique of waveform enrichment. The technique is general, such that it can be applied to the Lagrangian family of finite elements with specific waveform enrichment schemes, depending on the dominant modes of wave propagation in the physical system. A four-noded element for the Reissner-indlin plate is derived in this paper, which is free of shear locking. Such a locking-free property is achieved by removing the transverse displacement degrees of freedom from the element nodal variables and by recovering the same through a line integral and a weak constraint in the frequency domain. As a result, the frequency-dependent stiffness matrix and the mass matrix are obtained, which capture the higher frequency response with even coarse meshes, accurately. The steps involved in the numerical implementation of such element are discussed in details. Numerical studies on the performance of the proposed element are reported by considering a number of cases, which show very good accuracy and low computational cost. Copyright (C)006 John Wiley & Sons, Ltd.

An operator-splitting finite element method for the efficient parallel solution of multidimensional population balance systems

A finite element method for solving multidimensional population balance systems is proposed where the balance of fluid velocity, temperature and solute partial density is considered as a two-dimensional system and the balance of particle size distribution as a three-dimensional one. The method is based on a dimensional splitting into physical space and internal property variables. In addition, the operator splitting allows to decouple the equations for temperature, solute partial density and particle size distribution. Further, a nodal point based parallel finite element algorithm for multi-dimensional population balance systems is presented. The method is applied to study a crystallization process assuming, for simplicity, a size independent growth rate and neglecting agglomeration and breakage of particles. Simulations for different wall temperatures are performed to show the effect of cooling on the crystal growth. Although the method is described in detail only for the case of d=2 space and s=1 internal property variables it has the potential to be extendable to d+s variables, d=2, 3 and s >= 1. (C) 2011 Elsevier Ltd. All rights reserved.

Automatic finite element formulation and assembly of hyperelastic higher order structural models

The formulation of higher order structural models and their discretization using the finite element method is difficult owing to their complexity, especially in the presence of non-linearities. In this work a new algorithm for automating the formulation and assembly of hyperelastic higher-order structural finite elements is developed. A hierarchic series of kinematic models is proposed for modeling structures with special geometries and the algorithm is formulated to automate the study of this class of higher order structural models. The algorithm developed in this work sidesteps the need for an explicit derivation of the governing equations for the individual kinematic modes. Using a novel procedure involving a nodal degree-of-freedom based automatic assembly algorithm, automatic differentiation and higher dimensional quadrature, the relevant finite element matrices are directly computed from the variational statement of elasticity and the higher order kinematic model. Another significant feature of the proposed algorithm is that natural boundary conditions are implicitly handled for arbitrary higher order kinematic models. The validity algorithm is illustrated with examples involving linear elasticity and hyperelasticity. (C) 2013 Elsevier Inc. All rights reserved.

On the domain decomposition and transmission line modelling finite element method for time-domain induction motor analysis

This paper demonstrates how a finite element model which exploits domain decomposition is applied to the analysis of three-phase induction motors. It is shown that a significant gain in cpu time results when compared with standard finite element analysis. Aspects of the application of the method which are particular to induction motors are considered: the means of improving the convergence of the nonlinear finite element equations; the choice of symmetrical sub-domains; the modelling of relative movement; and the inclusion of periodic boundary conditions. © 1999 IEEE.

Lateral response of monopiles using centrifuge testing and finite element analysis

Offshore wind capacity is expected to grow exponentially over the next decade resulting in the production of a considerable amount of renewable energy. Monopiles are currently the most popular type of foundation for supporting offshore wind turbines in shallow to medium depth waters. In this paper, the load-deformation response of a 3.8 m diameter monopile installed in soft clays when subjected to axial and lateral loading is investigated using centrifuge testing and soil pore-fluid coupled three-dimensional finite element analysis. Monopile deformation is principally assessed in terms of its lateral displacements and bending moments. Its behaviour as a short rigid pile is discussed using concepts such as its rotation at mudline and the pile depth at which pivoting occurs. © 2014 Taylor & Francis Group.

An important pitfall of pseudo-static finite element analysis

Finite Element (FE) pseudo-static analysis can provide a good compromise between simplified methods of dynamic analysis and time domain analysis. The pseudo-static FE approach can accurately model the in situ, stresses prior to seismic loading (when it follows a static analysis simulating the construction sequence) is relatively simple and not as computationally expensive as the time domain approach. However this method should be used with caution as the results can be sensitive to the choice of the mesh dimensions. In this paper two simple examples of pseudo-static finite element analysis are examined parametrically, a homogeneous slope and a cantilever retaining wall, exploring the sensitivity of the pseudo-static analysis results on the adopted mesh size. The mesh dependence was found to be more pronounced for problems with high critical seismic coefficients values (e.g. gentle slopes or small walls), as in these cases a generalised layer failure mechanism is developed simultaneously with the slope or wall mechanism. In general the mesh width was found not to affect notably the predicted value of critical seismic coefficient but to have a major impact on the predicted movements. © 2012 Elsevier Ltd.

Comparison of finite element and finite volume methods application in geometrically nonlinear stress analysis

A novel three-dimensional finite volume (FV) procedure is described in detail for the analysis of geometrically nonlinear problems. The FV procedure is compared with the conventional finite element (FE) Galerkin approach. FV can be considered to be a particular case of the weighted residual method with a unit weighting function, where in the FE Galerkin method we use the shape function as weighting function. A Fortran code has been developed based on the finite volume cell vertex formulation. The formulation is tested on a number of geometrically nonlinear problems. In comparison with FE, the results reveal that FV can reach the FE results in a higher mesh density.

Dynamic load-balancing of finite element applications with the DRAMA library

The DRAMA library, developed within the European Commission funded (ESPRIT) project DRAMA, supports dynamic load-balancing for parallel (message-passing) mesh-based applications. The target applications are those with dynamic and solution-adaptive features. The focus within the DRAMA project was on finite element simulation codes for structural mechanics. An introduction to the DRAMA library will illustrate that the very general cost model and the interface designed specifically for application requirements provide simplified and effective access to a range of parallel partitioners. The main body of the paper will demonstrate the ability to provide dynamic load-balancing for parallel FEM problems that include: adaptive meshing, re-meshing, the need for multi-phase partitioning.