Tool wear is a significant problem for manufacturing companies and represents a major challenge in their operations, but it is also a way they can gain a competitive advantage. To do this it is important to set up a standard procedure to develop high performing tooling. This thesis outlines how the Finite Element (FE) method can be used to understand and develop tool geometry. FE based simulation, as a numerical method, is a reliable method to assess the performance of a cutting tool before conducting machining tests based on the force and temperature profile predicted by the FE model. Defining a mathematical model which can be used as a built-in algorithm for tool wear prediction is very challenging and time consuming. Instead there is a possibility of using other factors such as stress distribution and temperature profile and correlate them to tool wear. In this research, the performance of different tool edge radius in cutting has been studied through experiments and in parallel Updated Lagrangian Models have been developed through ABAQUS/EXPLICIT for various cutting conditions, and experimental data was used to validate the data that has been generated from the finite element models. These models are very convenient to develop and capable of being applied for other types of material and cutting conditions. Thus, they represent an efficient way to reduce the amount of experiments needed to improve a tooling, the machining process, and thereby provide an effective way to increase the machining productivity of manufacturing companies. / Thesis / Master of Applied Science (MASc)

Finite element analysis of laminated shells using a three-noded flat triangular shell element is presented. The flat shell element is obtained by combining the Discrete Kirchhoff Theory (DKT) plate bending element and a membrane element similar to the Allman element, but derived from the Linear Strain Triangular (LST) element. Though this combination has been employed in the literature for linear static analysis of laminated plates, the results presented are not adequate to ascertain that the element would perform well in the case of static and dynamic analysis of general shells. The element is first thoroughly tested for linear static analysis of laminated plates and shells and is extended for free vibration, thermal, and geometrically nonlinear analysis. The major drawback of the DKT plate bending element is that the transverse displacement is not explicitly defined within the interior of the element. Hence obtaining the consistent mass matrix or the derivatives of the transverse displacement that are required for forming the geometric stiffness matrix is not straight forward. This problem is alleviated by borrowing shape functions from other similar elements or using simple displacement fields. In the present research, free vibration analysis is performed both by using a lumped mass matrix and a so called consistent mass matrix, obtained by borrowing shape functions from an existing element, in order to compare the performance of the two methods. The geometrically nonlinear analysis is performed using an updated Lagrangian formulation employing Green strain and Second Piola-Kirchhoff (PK2) stress measures. A linear displacement field is used for the transverse displacement in order to compute the derivatives of the transverse displacement that are required to compute the geometric stiffness or the initial stress matrix. Several numerical examples are solved to demonstrate the accuracy of the formulation for both small and large rotation analysis of laminated plates and shells. The results are compared with those available in the existing literature and those obtained using the commercial finite element package ABAQUS and are found to be in good agreement. The element is employed for two main applications involving large flexible structures. The first application is the control of thermal deformations of a spherical mirror segment, which is a segment of a multi-segmented primary mirror used in a space telescope. The feasibility of controlling the surface distortions of the mirror segment due to arbitrary thermal fields, using discrete and distributed actuators, is studied. This kind of study was required for the design of a multi-segmented primary mirror of a next generation space telescope. The second application is the analysis of an inflatable structure, being considered by the US Army for housing vehicles and personnel. The tent structure is made up of membranes supported by arches stiffened by internal pressure. The updated Lagrangian formulation of the flat shell element has been developed primarily for the nonlinear analysis of the tent structure, since such a structure is expected to undergo large deformations and rotations under the action of environmental loads like the wind and snow loads. The wind load is modeled as a nonuniform pressure load and the snow load as lumped concentrated loads. Since the direction of the pressure load is assumed to be normal to the current configuration of the structure, it changes as the structure undergoes deformation. This is called the follower action. As a result, the pressure load is a function of the displacements and hence contributes to the tangent stiffness matrix in the case of geometrically nonlinear analysis. The thermal load also contributes to the system tangent stiffness matrix. In the case of the thermal load this contribution is similar to the initial stress matrix and hence no additional effort is required to compute this contribution. In the case of the pressure load, this contribution (called the pressure stiffness) is in general unsymmetric but can be systematically derived from the principle of virtual work. The follower effects of the pressure load have been included in the updated Lagrangian formulation of the flat shell element and have been validated using standard examples in the literature involving deformation-dependent pressure loads. The element can be used to obtain the nonlinear response of the tent structure under wind and snow loads. / Ph. D.

The goal of the present doctoral research is to create a theoretical framework and develop a numerical implementation for a shell finite element that can potentially achieve higher performance (i.e. combination of speed and accuracy) than current Continuum-based (CB) shell finite elements (FE), in particular in applications related to soft biological tissue dynamics. Specifically, this means complex and irregular geometries, large distortions and large bending deformations, and anisotropic incompressible hyperelastic material properties. The critical review of the underlying theories, formulations, and capabilities of the existing CB shell FE revealed that a general nonlinear CB shell FE with the abovementioned capabilities needs to be developed. Herein, we propose the theoretical framework of a new such CB shell FE for dynamic analysis using the total and the incremental updated Lagrangian (UL) formulations and explicit time integration. Specifically, we introduce the geometry and the kinematics of the proposed CB shell FE, as well as the matrices and constitutive relations which need to be evaluated for the total and the incremental UL formulations of the dynamic equilibrium equation. To verify the accuracy and efficiency of the proposed CB shell element, its large bending and distortion capabilities, as well as the accuracy of three different techniques presented for large strain analysis, we implemented the element in Matlab and tested its application in various geometries, with different material properties and loading conditions. The new high performance and accuracy element is shown to be insensitive to shear and membrane locking, and to initially irregular elements.

Small kinematics assumption in classical engineering has been in the center of consideration in structural analysis for decennaries. In the recent years the interest for sustainable and optimized structures, lightweight structures and new materials has grown rapidly as a consequence of desire to archive economical sustainability. These issues involve non-linear constitutive response of materials and can only be accessed on the basis of geometrically and materially non-linear analysis. Numerical simulations have become a conventional tool in modern engineering and have proven accuracy in computation and are on the verge of superseding time consuming and costly experiments.\newlineConsequently, this work presents a numerical computational framework for modeling of geometrically non-linear large deformation of isotropic and orthotropic materials under static and dynamic loading. The numerical model is applied on isotropic steel in plane strain and orthotropic wood in 3D under static and dynamic loading. In plane strain Total Lagrangian, Updated Lagrangian, Newmark-$\beta$ and Energy Conserving Algorithm time-integration methods are compared and evaluated. In 3D, a Total Lagrangian static approach and a Total Lagrangian based dynamic approach with Newmark-$\beta$ time-integration method is proposed to numerically predict deformation of wood under static and dynamic loading. The numerical model's accuracy is validated through an experiment where a knot-free pine wood board under large deformation is studied. The results indicate accuracy and capability of the numerical model in predicting static and dynamic behaviour of wood under large deformation. Contrastingly, classical engineering solution proves its inaccuracy and incapability of predicting kinematics of the wood board under studied conditions. / Små kinematikantaganden inom klassisk ingenjörsteknik har varit centralt för konstruktionslösningar under decennier. Under de senaste åren har intresset för hållbara och optimerade strukturer, lättviktskonstruktioner och nya material ökat kraftigt till följd av önskan att uppnå ekonomisk hållbarhet. Dessa nya konstruktionslösningar involverar icke-linjär konstitutiv respons hos material och kan endast studeras baserad på geometriskt och materiellt olinjär analys. Numeriska simuleringar har blivit ett konventionellt verktyg inom modern ingenjörsteknik och visat sig ge noggrannhet i beräkning och kan på sikt ersätta tidskrävande och kostsamma experiment.\newlineDetta examensarbete presenterar ett numeriskt beräkningsramverk för modellering av geometrisk olinjäritet med stora deformationer hos isotropa och ortotropa material vid statisk och dynamisk belastning. Den numeriska modellen appliceras på isotropiskt stål i plantöjning och ortotropisk trä i 3D vid statisk och dynamisk belastning. I fallet med plantöjning jämförs och utvärderas den Totala Lagrangianen, Uppdaterade Lagrangianen, Newmark-$\beta$ och Energi Konserverings Algoritm metoderna. I 3D föreslås en statisk Total Lagrangian metod och en dynamisk Total Lagrangian-baserad metod med Newmark-$\beta$ tidsintegreringsmetod för att numeriskt förutse statisk och dynamisk deformation hos trä. Den numeriska modellens noggrannhet valideras genom ett experiment där en kvistfri furuplanka studeras under stora deformationer. Resultaten bekräftar noggrannhet och förmåga hos den numeriska modellen att förutse statiska och dynamiska processer hos trä vid stora deformationer. Däremot, visar klassisk ingenjörslösning brist på förmåga att förutse trä plankans kinematik under studerade förhållanden.