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**1 - 10**of**10**### Modelling Requirements for Computer Simulation of Metal Machining

"... Machining modelling efforts are summarised and some important shortcomings of these are presented. The reasons for these shortcomings have been investigated. The investigations are based on machining simulation research and accompanying experimental studies. The reasons are found to be mainly in the ..."

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Machining modelling efforts are summarised and some important shortcomings of these are presented. The reasons for these shortcomings have been investigated. The investigations are based on machining simulation research and accompanying experimental studies. The reasons are found to be mainly in the approaches taken towards modelling the mesh and boundary conditions, the flow stress of the workpiece material and the frictional properties at the interface between the chip and the cutting tool. The handlings of the extremely high temperature increases and the mechanism taking place during separation of the chip from the workpiece by the tool are also among the significant reasons. The aim of this paper is to present some solutions towards modelling these aspects of machining.

### Test Functions for Elliptic Problems Satisfying Linear Essential Edge Conditions on Both Convex and Concave Polygons

, 2003

"... Interpolations which are smooth and bounded can be constructed over any two dimensional polygonal domain, including those with concavities and inclusions. Like boundary element test functions, they depend only on the boundary values. Unlike the boundary element method formulations, they satisfy line ..."

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Interpolations which are smooth and bounded can be constructed over any two dimensional polygonal domain, including those with concavities and inclusions. Like boundary element test functions, they depend only on the boundary values. Unlike the boundary element method formulations, they satisfy linear essential boundary conditions exactly and do not depend on a Greens' function solution to the governing field equation. In other words, they are Ritz type coordinate functions which apply to any polygonal domain. The interpolations satisfy element level constancy and linear patch tests and perform well in approximation of potential field solutions. Similar functions, applicable only to convex polygons, have been applied successfully to biomedical problems including skull growth and heart function analyses. No smooth kinematic concave polygonal element description of any type is presented in the available finite element, boundary element or computational geometry literature.

### Finite Element Analysis of Slab and a Comparative Study with Others Analytical Solution

"... Slabs are one of the most widely used structural elements. The function of slabs is to resist loads normal to their plane. In many structures, in addition to support transverse load, the slab also forms an integral portion of the structural frame to resist lateral load. Inspite of their widespread u ..."

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Slabs are one of the most widely used structural elements. The function of slabs is to resist loads normal to their plane. In many structures, in addition to support transverse load, the slab also forms an integral portion of the structural frame to resist lateral load. Inspite of their widespread use, there has never been a universally accepted method of designing all slabs systems. The paper presents finite element analysis of slabs. The finite element method is chosen as this is more powerful and versatile compared to other numerical methods. A slab element is developed on the basis of conventional slab theory expressed in terms of rectangular co-ordinates and displacement. The element incorporates 20 degree of freedom, namely, normal displacement with its first derivatives along longitudinal and transverse direction respectively and two tangential displacements. A computer program is developed for solution of finite element equations as well as to check rigid body modes and to obtain the results. The results are compared with analytical solution and previously developed finite element solution with the help of a table.

### Approved by:

, 2002

"... (Under the direction of Henry Fuchs.) This work focuses on the simulation of mechanical contact between nonlinearly elastic objects such as the components of the human body. The computation of the reaction forces that act on the contact surfaces (contact forces) is the key for designing a reliable c ..."

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(Under the direction of Henry Fuchs.) This work focuses on the simulation of mechanical contact between nonlinearly elastic objects such as the components of the human body. The computation of the reaction forces that act on the contact surfaces (contact forces) is the key for designing a reliable contact handling algorithm. In traditional methods, contact forces are often defined as discontinuous functions of deformation, which leads to poor convergence characteristics. This problem becomes especially serious in areas with complicated self-contact such as skin folds. I introduce a novel penalty method for finite element simulation based on the concept of material depth, which is the distance between a particle inside an object and the object’s boundary. By linearly interpolating pre-computed material depths at node points, contact forces can be analytically integrated over contact surfaces without raising the computational cost. The continuity achieved by this formulation reduces oscillation and artificial acceleration resulting in a more reliable simulation algorithm. This algorithm is implemented as part of an implicit finite element program for static,

### unknown title

, 1999

"... A numerical investigation of some problems associated with the biharmonic operator ..."

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A numerical investigation of some problems associated with the biharmonic operator

### Structural Dynamic Analysis and Model Updating for a Welded Structure made from Thin Steel Sheets

, 2012

"... Modern large, complex, engineering structures normally encompass a number of substructures which are assembled together by several types of joints. Despite, the highly sophisticated finite element method that is widely used to predict dynamic behaviour of assembled complete structures, the predicted ..."

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Modern large, complex, engineering structures normally encompass a number of substructures which are assembled together by several types of joints. Despite, the highly sophisticated finite element method that is widely used to predict dynamic behaviour of assembled complete structures, the predicted results achieved, of assembled structures are often far from the experimental observation in comparison with those of substructures. The inaccuracy of prediction is believed to be largely due to invalid assumptions about the input data on the initial finite element models, particularly those on joints, boundary conditions and also loads. Therefore, model updating methods are usually used to improve the initial finite element models by using the experimentally observed results. This thesis is concerned with the application of model updating methods to a welded structure that consists of several substructures made from thin steel sheets that are assembled together by a number of spot welds. However, the welded structure with a large surface area is susceptible to initial curvature due to its low

### Real-time Simulation of Deformable Objects

"... In recent years there has been a growing interest in computer-based surgical plan-ning, virtual-reality enabled training of medical procedures, and computer gam-ing all involving non-rigid deformable objects. High-fidelity simulations of haptic interaction with deformable objects is computationally ..."

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In recent years there has been a growing interest in computer-based surgical plan-ning, virtual-reality enabled training of medical procedures, and computer gam-ing all involving non-rigid deformable objects. High-fidelity simulations of haptic interaction with deformable objects is computationally demanding. The Finite El-ement Method (FEM) is known to produce relatively accurate solution for contin-uum mechanics-based models of soft-object deformation. Linear elastic FE models require solving a large sparse system of equations. The solution accuracy can be improved by increasing the resolution of the finite element mesh resulting in a larger number of equations and hence greater computational complexity. Depend-ing on the mechanical characteristics of the soft-object, to maintain stability and high fidelity in haptic interaction, the update rate should be in the range of 100-1000Hz. This, for example, means that for a moderately-sized three-dimensional mesh of 6000 nodes, a set of 18000 linear equations must be solved within 1-10ms. In this thesis, hardware-based parallel computing is proposed for finite-element

### Methods in Engineering State of the art reviews Origins, Milestones and Directions of the Finite Element Method – A Personal View†

"... The article traces the important steps of the development of the finite element method from its origins in aircraft structural engineering to the present day, where it provides the essential tool for solution of a great variety of problems in engineering and physics. The emphasis and the choice of t ..."

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The article traces the important steps of the development of the finite element method from its origins in aircraft structural engineering to the present day, where it provides the essential tool for solution of a great variety of problems in engineering and physics. The emphasis and the choice of the “landmarks ” stresses the aspects which are general and essentially of mathematical nature applicable to a wide range of situations. For this reason no mention is made of perhaps equally important developments to new application fields such as metal forming, electromagnetics, geomechanics etc. 1.

### Duality-Based Adaptive Finite Element Methods with Application to Time-Dependent Problems

, 2010

"... To simulate real world problems modeled by differential equations, it is often not sufficient to consider and tackle a single equation. Rather, com-plex phenomena are modeled by several partial differential equations that are coupled to each other. For example, a heart beat involve electric ac-tivit ..."

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To simulate real world problems modeled by differential equations, it is often not sufficient to consider and tackle a single equation. Rather, com-plex phenomena are modeled by several partial differential equations that are coupled to each other. For example, a heart beat involve electric ac-tivity, mechanics of the movement of the walls and valves, as well as blood flow – a true multiphysics problem. There may also be ordinary differential equations modeling the reactions on a cellular level, and these may act on a much finer scale in both space and time. Determining efficient and accurate simulation tools for such multiscalar multiphysics problems is a challenge. The five scientific papers constituting this thesis investigate and present solutions to issues regarding accurate and efficient simulation using adaptive finite element methods. These include handling local accuracy through submodeling, analyzing error propagation in time-dependent multiphysics problems, developing efficient algorithms for adaptivity in time and space, and deriving error analysis for coupled PDE-ODE systems. In all these examples, the error is analyzed and controlled using the framework of dual-weighted residuals, and the spatial meshes are handled using octree based data structures. However, few realistic geometries fit such grid and to address this issue a discontinuous Galerkin Nitsche method is presented and analyzed.