Finite Element Algorithms for Computational Biomechanics of the Brain

Patient-specific non-linear finite element modelling for predicting soft organ deformation in real-time; Application to non-rigid neuroimage registration

This paper deals with the estimation of second order wave excitation forces on a free floating triple-hull barge using software developed based on finite element method. The wave-hull interaction nonlinear problem is presented here using the perturbation method, where potential flow theory is used. In the finite element model, the absorbing or nonreflecting far boundary condition is applied at a truncated surface in the form of boundary damper. The software developed for the solution of this nonlinear problem is validated for two and three-dimensional cases for which analytical and other numerical solutions are known. A convergence study on the three-dimensional cylinder problem is carried out to derive a guideline in selecting finite element mesh density and its grading. A triple-hull barge problem is selected here as a practical problem to study the nonlinear wave effects on the forces and motions. A grid independent study on this problem is carried out by using four finite element meshes of different density and grading. The optimum mesh selected from this study is used for further analysis of the problem. Bandwidth optimization is carried out on the generated meshes in order to reduce the computational effort, as the finite element algorithm used here is based on the banded solver technique. The second order wave excitation forces and moments on the barge estimated for different wave steepness (H/Lw - 0.08 to 0.012) in oblique sea condition shows that the second order surge and heave forces amounts up to 49% and 17.5% respectively and the second order yaw moment up to 39% when compared with the first order (linear) wave forces. Similar trend is observed for the forces and moments in beam sea and head sea conditions.

On the mechanical properties of materials of construction

This study investigates the influence of frictional properties between the spring wire and coiling tools on the deformation behavior during the coiling process with coiling pin system, using dynamic explicit finite element analysis with ANSYS LS-DYNA. The analysis focused on varying the coefficients of dynamic friction between the wire and four key tools: the wire guide, first coiling pin, second coiling pin, and pitch tool. Results revealed that the average coil diameter, stress distribution, and compressive axial force during forming were significantly affected by frictional conditions, particularly those at the second coiling pin. A reduction in the friction coefficient at the second coiling pin led to increased coil diameters and decreased stress and axial force. These findings indicate that friction at the second pin predominantly governs coil shaping and significantly impacts spring dimensions. Furthermore, deteriorated sliding properties due to inadequate lubrication may cause dimensional variation or even failure during forming. This analysis emphasizes the critical role of wire-tool friction management in ensuring spring quality and consistency.

This paper presents an overview of research and development efforts that are currently being devoted to integrate large deformation finite element formulations with flexible multibody system algorithms. The goal is to develop computer simulation capabilities for the analysis of physics and engineering models with significant details. The successful development of such new and integrated algorithms will also allow modeling and simulation of systems that cannot be solved using existing computer algorithms and codes. One of the main difficulties encountered in this integration process is attributed to the fact that the solution procedures used in finite element codes differ significantly from those used in general-purpose flexible multibody system codes. Finite element methods employ the corotational formulations that are often used with incremental solution procedures. Flexible multibody computer codes, on the other hand, do not, in general, use incremental solution procedures. Three approaches are currently being explored by academic institutions and the software industry. In the first approach, gluing algorithms that aim at performing successful simulations by establishing an interface between existing codes are used. Using different coordinates and synchronizing the time stepping are among several challenging problems that are encountered when gluing algorithms are used. In the second approach, multibody system capabilities are implemented in existing finite element algorithms that are based on large rotation vector formulations. For the most part, corotational formulations and incremental solution procedures are used in this case. In the third approach, a new large deformation finite element formulation that can be successfully implemented in flexible multibody system computer algorithms that employ nonincremental solution procedures is introduced. The approach that is now being developed in several institutions is based on the finite element absolute nodal coordinate formulation. Such a formulation can be systematically implemented in general-purpose flexible multibody system computer algorithms. Nonlinear constraint equations that describe mechanical joints between different bodies can be formulated in terms of the absolute coordinates in a straightforward manner. The coupling between the motion of rigid, flexible, and very flexible bodies can also be accurately described. The successful integration of large deformation finite element and multibody system algorithms will lead to a new generation of computer codes that can be systematical and efficiently used in the analysis of many engineering applications.

A novel meshing algorithm for dynamic finite element analysis

The new second-order two-scale (SOTS) finite element algorithm is developed for the dynamic thermo-mechanical coupling problems in axisymmetric and spherical symmetric structures made of composite materials. The axisymmetric structure considered is periodic in both radial and axial directions and homogeneous in circumferential direction. The spherical symmetric structure is only periodic in radial direction. The dynamic thermo-mechanical coupling model is presented and the equivalent compact form is derived. Then, the cell problems, effective material coefficients and the homogenized thermo-mechanical coupling problem are obtained successively by the second-order asymptotic expansion of the temperature increment and displacement. The homogenized material obtained is manifested with the anisotropic property in the circumferential direction. The explicit expressions of the homogenized coefficients in the plane axisymmetric and spherical symmetric cases are given and both the derivation of the analytical solutions of the cell functions and the quasi-static thermoelasticity problems are discussed. Based on the SOTS method, the corresponding finite-element procedure is presented and the unconditionally stable implicit algorithm is established. Some numerical examples are solved and the mutual interaction between the temperature and displacement field is studied under the condition of structural vibration. The computational results demonstrate that the second-order asymptotic analysis finite-element algorithm is feasible and effective in simulating and predicting the dynamic thermo-mechanical behaviors of the composite materials with small periodic configurations in axisymmetric and spherical symmetric structures. This may provide a vital computational tool for analyzing composite material internal temperature distribution and structural deformation induced by the dynamic thermo-mechanical coupling response under strong aerothermodynamic environment. Second-order two-scale (SOTS) expansions for dynamic thermo-mechanical coupling problems in symmetric structure are obtained.SOTS finite element algorithm is proposed and unconditional stable implicit scheme is established.Anisotropic material is obtained by homogenization with enhanced strength and minor thermal expansion in circumferential direction.The mutual interaction and simultaneous vibration of the temperature and displacement field are simulated.A new computational tool is presented for analyzing thermo-mechanical response of composites under strong aerothermodynamic environment.

Introducing the hierarchy into cellular materials has attracted increasing attention in the effort to pursue improved absorbed-energy abilities and impact resistance. In this paper, the dynamic crushing properties and energy absorption capacities of joint-based hierarchical honeycombs with different topologies were explored by means of explicit dynamic finite element (FE) analysis using ANSYS/LS-DYNA. Four types of joint-based hierarchical honeycombs with uniform cell-wall thickness were firstly constructed by substituting each vertex of regular honeycombs with a smaller self-similar cell (hexagon or square). The respective influences of hierarchical parameters and impact velocities on in-plane dynamic deformation modes, mechanical characteristic and energy absorption of joint-based hierarchical honeycombs were discussed. Research results showed that the hierarchy had a far greater influence on the in-plane deformation modes of honeycombs. Compared with regular honeycombs, the dynamic plateau stress and specific energy absorption of joint-based hierarchical honeycombs can be improved if the proper hierarchical parameters were chosen. Adding the joint-based hierarchy into regular honeycombs can enhance the crushing stress efficiency (CSE) of the specimens. In addition, by introducing a non-dimensional dynamic sensitivity index, the dynamic shock enhancement of hierarchical honeycombs was also investigated. These researches are useful for the multi-objective dynamic optimization design and controllable properties of cellular materials.

Feedback control has become a crucial tool in the research on magnetic confinement of plasmas for achieving controlled nuclear fusion. This thesis presents a novel plasma feedback control system that, for the first time, employs a Graphics Processing Unit (GPU) for microsecond-latency, real-time control computations. This novel application area for GPU computing is opened up by a new system architecture that is optimized for low-latency computations on less than kilobyte sized data samples as they occur in typical plasma control algorithms. In contrast to traditional GPU computing approaches that target complex, high-throughput computations with massive amounts of data, the architecture presented in this thesis uses the GPU as the primary processing unit rather than as an auxiliary of the CPU, and data is transferred from A-D/D-A converters directly into GPU memory using peer-to-peer PCI Express transfers. The described design has been implemented in a new, GPU-based control system for the High-Beta Tokamak – Extended Pulse (HBT-EP) device. The system is built from commodity hardware and uses an NVIDIA GeForce GPU and D-TACQ A-D/D-A converters providing a total of 96 input and 64 output channels. The system is able to run with sampling periods down to 4 μs and latencies down to 8 μs. The GPU provides a total processing power of 1.5 x 1012 floating point operations per second. To illustrate the performance and versatility of both the general architecture and concrete implementation, a new control algorithm has been developed. The algorithm is designed for the control of multiple rotating magnetic perturbations in situations where the plasma equilibrium is not known exactly and features an adaptive system model: instead of requiring the rotation frequencies and growth rates embedded in the system model to be set a priori, the adaptive algorithm derives these parameters from the evolution of the perturbation amplitudes themselves. This results in non-linear control computations with high computational demands, but is handled easily by the GPU based system. Both digital processing latency and an arbitrary multi-pole response of amplifiers and control coils is fully taken into account for the generation of control signals. To separate sensor signals into perturbed and equilibrium components without knowledge of the equilibrium fields, a new separation method based on biorthogonal decomposition is introduced and used to derive a filter that performs the separation in real-time. The control algorithm has been implemented and tested on the new, GPU-based feedback control system of the HBT-EP tokamak. In this instance, the algorithm was set up to control four rotating n = 1 perturbations at different poloidal angles. The perturbations were treated as coupled in frequency but independent in amplitude and phase, so that the system effectively controls a helical n = 1 perturbation with unknown poloidal spectrum. Depending on the plasma's edge safety factor and rotation frequency, the control system is shown to be able to suppress the amplitude of the dominant 8 kHz mode by up to 60% or amplify the saturated amplitude by a factor of up to two. Intermediate feedback phases combine suppression and amplification with a speed up or slow down of the mode rotation frequency. Increasing feedback gain results in the excitation of an additional, slowly rotating 1.4 kHz mode without further effects on the 8 kHz mode. The feedback performance is found to exceed previous results obtained with an FPGA- and Kalman-filter based control system without requiring any tuning of system model parameters. Experimental results are compared with simulations based on a combination of the Boozer surface current model and the Fitzpatrick-Aydemir model. Within the subset of phenomena that can be represented by the model as well as determined experimentally, qualitative agreement is found.

In the processing of composites, fibre reinforcement is draped over complex three dimensional geometries, yielding local variations in the fibre volume fraction and fibre orientation with subsequent effects on the permeability of the reinforcement during resin infiltration and on the properties of the composite product. This study presents computer simulations of the draping of fabrics by following a mechanical, finite element approach. The fabric is considered as a solid continuum with mechanical properties and friction properties at interfaces. The problem is solved by applying an explicit dynamic finite element analysis. In order to incorporate the large shear deformation of fabric during draping, an updated material behaviour law was formulated on the basis of changing fibre directions. The model was implemented in a user computer subroutine and tested first in case-studies of simple in-plane shear where the predictions were also compared with experimental data from a picture frame type of shear test. Thereafter, numerical simulations focused on the draping of a fabric in a “hat” shaped mould, comprising a hemispherical cup with a wide flat rim. The predictions were compared with predictions from similar simulations without the updated material behaviour law, experimental data and predictions from a “fishnet” algorithm.

For electrical impedance tomography (EIT) of brain, the use of anatomically accurate and patient-specific finite element (FE) mesh has been shown to confer significant improvements in the quality of image reconstruction. But, given the lack of a rapid method to achieve the accurate anatomic geometry of the head, the generation of patient-specifc mesh is time-comsuming. In this paper, a m odified fuzzy c-means algorithm based on no n-local means method is performed to implement the segmentation of different layers in the head based on head CT images. This algorithm showed a better effect, especially an accurate recognition of the ventricles and a suitable performance dealing with noise. And the FE mesh established according to the segmentation results is valid ated in computational simulation. So a rapid practicable method can be provided for the generation of patient-specific FE mesh of the human head that is suitable for brain EIT. Keyword: Computerized tomography, image segmentation, mesh generation, electrical impedance tomography

The second edition of Applied Mechanics of Solids provides a concise description of all the concepts needed to predict how solid materials deform and fail under stress. With its companion volume of solved example problems, it is an invaluable class textbook or reference for personal study or review. With the aid of computer simulations, design engineers can predict stresses, deformation, and failure in structural, mechanical, and bio-mechanical components with a few keystrokes. But simulations are built on sophisticated mathematics, physics, and numerical methods, and always involve some judicious approximations. Engineers need a thorough grasp of these concepts to know how to set up their simulations correctly and to interpret their predictions.   This book contains all the theory they need to make the best use of their simulations. Beginning with a description of the physical and mathematical laws that govern deformation in solids, the text presents models of material behavior; solutions to important boundary value problems using classical methods of analysis; a detailed description of the finite element method; fracture mechanics and failure analysis; as well as structural theories of rods, plates and shells.  All chapters in this new edition contain additional material, but the most substantial changes are to Chapter 8: “Finite Element Analysis: Theory and Implementation,” which now covers topics such as locking-resistant finite elements for simulations of solids subjected to large deformations; structural elements (trusses, beams, and plates); as well as methods for enforcing constraints in finite element simulations, cohesive zone models of interface fracture, and contact elements.  In addition, a new companion volume provides over 400 example problems with their solutions. The text is supplemented by example finite element codes posted on GitHub, which demonstrate all the finite element algorithms described in the text.

Sensitivity analysis with the modified Heaviside function for the optimal layout design of multi-component systems

Aimed to solve current collision problems between car head and truck rear, collision simulation of a novel type multistage rear protector is achieved, structure has been designed and optimized before. Based on conservation of energy theorem and regulations of dynamic collision test, dynamic explicit finite element analysis method is applied for investigate the device. It is shown that the peak acceleration of the car body is significantly decreased and collision safety is greatly improved when the rear protector is adopted. Through the collision simulation results of dynamic acceleration and maximum deformation, it is indicated that the novel multistage rear protector has excellent energy absorption capability, not only reducing occupant injury from collision but also improving collision compatibility during the car head to truck rear collision.

A multiscale soft-contact modelling method for rough surfaces in contact with coupled slipping/sliding and rolling