A Material Point Method for Simulating Frictional Contact with Diverse Materials

We present an extension to the Material Point Method (MPM) for simulating elastic objects with various co-dimensions like hair (1D), thin shells (2D), and volumetric objects (3D). We simulate thin shells with frictional contact using a combination of MPM and subdivision finite elements. The shell kinematics are assumed to follow a continuum shell model which is decomposed into a Kirchhoff-Love motion that rotates the mid-surface normals followed by shearing and compression/extension of the material along the mid-surface normal. We use this decomposition to design an elastoplastic constitutive model to resolve frictional contact by decoupling resistance to contact and shearing from the bending resistance components of stress. We show that by resolving frictional contact with a continuum approach, our hybrid Lagrangian/Eulerian approach is capable of simulating challenging shell contact scenarios with hundreds of thousands to millions of degrees of freedom. Furthermore our technique naturally couples with other traditional MPM methods for simulating granular materials. Without the need for collision detection or resolution, our method runs in a few minutes per frame in these high resolution examples. For the simulation of hair and volumetric elastic objects, we utilize a Lagrangian mesh for internal force computation and an Eulerian mesh for self collision as well as coupling with external materials. While the updated Lagrangian discretization where the Eulerian grid degrees of freedom are used to take variations of the potential energy is effective in simulating thin shells, its frictional contact response strategy does not generalize to volumetric objects. Therefore, we develop a hybrid approach that retains Lagrangian degrees of freedom while still allowing for natural coupling with other materials simulated with traditional MPM. We demonstrate the efficacy of our technique with examples that involve elastic soft tissues coupled with kinematic skeletons, extreme deformation, and coupling with multiple elastoplastic materials. Our approach also naturally allows for two-way rigid body coupling

The Material Point Method for Solid and Fluid Simulation

The Material Point Method (MPM) has shown its high potential for physics-based simulation in the area of computer graphics. In this dissertation, we introduce a couple of improvements to the traditional MPM for different applications and demonstrate the advantages of our methods over the previous methods.First, we present a generalized transfer scheme for the hybrid Eulerian/Lagrangian method: the Polynomial Particle-In-Cell Method (PolyPIC). PolyPIC improves kinetic energy conservation during transfers, which leads to better vorticity resolution in fluid simulations and less numerical damping in elastoplasticity simulations. Our transfers are designed to select particle-wise polynomial approximations to the grid velocity that are optimal in the local mass-weighted L2 norm. Indeed our notion of transfers reproduces the original Particle-In-Cell Method (PIC) and recent Affine Particle-In-Cell Method (APIC). Furthermore, we derive a polynomial basis that is mass orthogonal to facilitate the rapid solution of the optimality condition. Our method applies to both of the collocated and staggered grid.As the second contribution, we present a novel method for the simulation of thin shells with frictional contact using a combination of MPM and subdivision finite elements. The shell kinematics are assumed to follow a continuum shell model which is decomposed into a Kirchhoff-Love motion that rotates the mid-surface normals followed by shearing and compression/extension of the material along the mid-surface normal. We use this decomposition to design an elastoplastic constitutive model to resolve frictional contact by decoupling resistance to contact and shearing from the bending resistance components of stress. We show that by resolving frictional contact with a continuum approach, our hybrid Lagrangian/Eulerian approach is capable of simulating challenging shell contact scenarios with hundreds of thousands to millions of degrees of freedom. Without the need for collision detection or resolution, our method runs in a few minutes per frame in these high-resolution examples. Furthermore, we show that our technique naturally couples with other traditional MPM methods for simulating granular and related materials.In the third part, we present a new hybrid Lagrangian Material Point Method for simulating volumetric objects with frictional contact. The resolution of frictional contact in the thin shell simulation cannot be generalized to the case of volumetric materials directly. Also, even though MPM allows for the natural simulation of hyperelastic materials represented with Lagrangian meshes, it usually coarsens the degrees of freedom of the Lagrangian mesh and can lead to artifacts, e.g., numerical cohesion. We demonstrate that our hybrid method can efficiently resolve these issues. We show the efficacy of our technique with examples that involve elastic soft tissues coupled with kinematic skeletons, extreme deformation, and coupling with various elastoplastic materials. Our approach also naturally allows for two-way rigid body coupling

Dynamic Inelastic Behaviour of Ship Plates in Collision

This thesis consists of eight chapters. In the first of these the literature on the structural aspects of ship collision is reviewed in terms of the specific topic in this field. Emphasis is placed on the structural response in collision in which several important aspects are addressed, such as, Minorsky's method, static and dynamic approach, impact force, dynamic effects and failure mode. Based on the Variational Finite Difference Method, a numerical model of dynamic inelastic response of plates impacted by a rigid knife indentor is developed in the second chapter. The numerical model includes the influence of finite transverse displacement, axial restraints, bending moments, material elasticity and strain hardening. The struck plate and rigid striker are coupled in the numerical simulation, with the deformation, strain, stress and impact force as output of the calculation. Chapter 3 presents the experimental investigation of clamped rectangular plates impacted by a knife edge indentor. A series of impact tests are conducted on aluminium and steel plates. The plate specimens are struck by a rigid knife edge indentor sliding down from a runway, and the impact loading is repeatedly applied to each plate until plate failure. Detailed experimental results are reported on impact and rebound velocities, permanent deformation, acceleration, dynamic strains and failure modes both for single impact and for repeated impacts. Different stages of plate failure are identified based on the dynamic strain recording. For the plate subjected to a number of identical impacts no pseudo-shakedown phenomenon is observed in the test. The influence of boundary conditions caused by in-plane sliding is also investigated. In chapter 4 the numerical approach proposed in chapter 2 is used to simulate the collision process of an aluminium plate impacted by a knife edge indentor. Numerical results provide a full picture of the response of the clamped rectangular plate under dynamic loading, giving information on the impact force, deformation, stress and strain history and distribution in the plate. Correlations are performed with the experimental results on the plate impact test described in chapter 3 as well as on the test of a small scale ship model which was conducted in the Department during 1981-1982. Very good agreement is reached. Parametric studies are made in chapter 5 on some important parameters for ship collision, such as mass and impact velocity of the striking bow, the length of vertical bow, the struck plate length and width, and plate thickness. As an application of the numerical work, critical speed for a longitudinally framed tanker struck by a rigid vertical bow is also investigated. Chapters 6 and 7 contain analytical solutions based on the Rigid Perfectly Plastic Method for single impact and repeated impacts respectively. An approximate theoretical procedure is developed to give the lower and upper bounds of the dynamic plastic solution to the impacted rectangular plate with finite deflections. The analytical solution obtained is compared with the experimental results and predictions of numerical program. It is found that no pseudo-shakedown occurs for the plate subjected to a number of identical impacts. Finally, conclusions and suggestions for further work are given in chapter 8

Mechanics of dented orthogonally stiffened cylinders

Imperial Users onl

Application of optimization techniques to vehicle design: A review

The work that has been done in the last decade or so in the application of optimization techniques to vehicle design is discussed. Much of the work reviewed deals with the design of body or suspension (chassis) components for reduced weight. Also reviewed are studies dealing with system optimization problems for improved functional performance, such as ride or handling. In reviewing the work on the use of optimization techniques, one notes the transition from the rare mention of the methods in the 70's to an increased effort in the early 80's. Efficient and convenient optimization and analysis tools still need to be developed so that they can be regularly applied in the early design stage of the vehicle development cycle to be most effective. Based on the reported applications, an attempt is made to assess the potential for automotive application of optimization techniques. The major issue involved remains the creation of quantifiable means of analysis to be used in vehicle design. The conventional process of vehicle design still contains much experience-based input because it has not yet proven possible to quantify all important constraints. This restraint on the part of the analysis will continue to be a major limiting factor in application of optimization to vehicle design

Design Approximations for Offshore Tubulars Against Collisions

The aim of this study is to derive simple design formulae for estimating the probable extent of damage to offshore tubular members due to lateral impacts, and for evaluating the residual strength of damaged tubular members subjected to combined axial compression and hydrostatic pressure. Existing models and methods are reviewed for predicting the probability of offshore collisions and consequential probable extents of damage, and for evaluating the residual strength of damaged members. Lateral impact tests are reported conducted on small-scale tubes having simply supported roller end conditions. The aim of the tests was to provide more realistic experimental information for local denting deformation of the tube wall at the point of impact and overall bending deformation of the tubular member as a beam under lateral impact. A simple numerical model is developed for simulating the dynamic response of a tubular member having simply supported roller end conditions. In the analysis, the tubular member is reduced to a spring-mass system with two degrees-of-freedom, one for local denting and the other for overall bending. Strain-rate sensitivity of the material and other dynamic effects upon the response of the tubular member have been considered by multiplying an empirically derived modification factor to the spring coefficient for overall bending. Combined axial compression and hydrostatic pressure loading tests are also conducted on damaged tubes whose form of damage are realistic. An analytical method is also developed to evaluate the residual strength of damaged tubular members under combined axial compression and hydrostatic pressure. The method involves two separate phases of calculation: derivation of bending moment - external axial compression - hydrostatic pressure - curvature relationships for dented tubular cross-sections using the tangent stiffness method; and determination of the residual strength of a damaged tubular member using the bending moment - curvature relationship based on the Newmark integration method. Rigorous parametric studies are performed using the theoretical models which have been validated with the experimental results obtained from the tests conducted as part of this study and other test data available in the literature. Finally, simple design formulae are derived using the parametric study results. A direct fit is attempted for design equations to predict the probable extent of damage to unstiffened tubular members subjected to lateral impacts, while the Perry formula is adopted as the basis of a formulation to estimate the residual strength of damaged tubular members under combined axial compression and hydrostatic pressure. Conclusions regarding the experimental and theoretical studies and the proposed design formulae are included, and an extension to this study is proposed in order for the design formulae to directly be applicable to the design of offshore structures against collisions. An approximate equation is presented in Appendix 1 for bending moment-external axial compression - hydrostatic pressure - curvature relationships of damaged tubular cross-sections. In Appendix 2 an approximate expression is derived for von Mises elastic buckling pressure of circular cylinder under pure radial pressure Appendix 3 describes the derivation procedure of a strength formulation for ring-stiffened cylindrical shells under combined axial loading and radial pressure, where the quadratic Merchant - Rankine formula in generalised form is adopted as the basis of the formulation. Volume II of this thesis is ref. 82 and contains the full experimental report and test data for the lateral impact tests

Overtrawlability and Mechanical Damage of Pipe-in-Pipe

Ph.DDOCTOR OF PHILOSOPH

Behavior of X60 Line Pipe under Combined Axial and Transverse Loads with Internal Pressure

Buried pipeline may be subjected to various complex combinations of forces and deformations. As a result, localized curvature and strains may occur in the pipe wall and wrinkle may form. The wrinkled pipeline may then develop a rupture and lose its structural integrity if it is subjected to further sustained deformation and/or load. This research program was designed to evaluate the post-wrinkling behaviour and structural integrity of wrinkled pipeline subjected to lateral and axial loads and internal pressure. This research program included both experimental and numerical studies. This study shows that a pipe does not fail in rupture if the pipe is subjected to an axisymmetric axial monotonic deformation and wrinkle is developed. However, a rupture is developed in the wrinkle region if the wrinkled pipe is subjected to lateral deformation. Parametric studies were also undertaken to understand the effect of D/t, and internal pressure on pipe failure mode

Numerical Assessment of FPSO Platform Behaviour in Ship Collision

Offshore platforms may potentially collide with vessels of various types, including visiting ships such as supply ships and passing ships. The most critical and relevant conditions, including the analysis and design approaches are introduced. Different ship types having different displacements and structural designs exert different vessel impact loads on impacted structures. This paper presents the findings of collision impact analyses of the side shell panel, bow and stern structures of Floating Production Storage Offloading (FPSO) platforms in case of impact, e.g. by a supply vessel or methanol tanker. As collision impact simulations continue to be conducted conservatively, the colliding positions of the striking vessel are presumed to be  bow and stern only, with side force. In order to assess hull strength in collision events, non-linear FE simulations were performed by means of the MSC / DYTRAN tool, as these collision events result in more complex reactions. The degree of hull damage suffered by an FPSO vessel in different collision scenarios and at varying impact energy levels was determined in accordance with the NORSOK N-004 standard guidelines. Post-collision analyses were conducted to establish the structural integrity of the damaged hull after being exposed to environmental conditions for one year. The reduction of hull girder strength associated with the worst damage was evaluated and accounted for in the present study, providing no further damage occurs. Furthermore, the acceptance criteria for evaluation and corresponding consequences are calculated and discussed in detail. Finally, the findings from the present paper will help clarify the impact response of offshore structures and evaluation approaches and give valuable guidance for the design and operation of FPSO platforms