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Dissertations / Theses on the topic 'Radical point interpolation method'

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Author: Grafiati

Published: 10 December 2022

Last updated: 28 January 2023

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1

Yildirim, Okan. "Radial Point Interpolation Method For Plane Elasticity Problems." Master's thesis, METU, 2010. http://etd.lib.metu.edu.tr/upload/12612537/index.pdf.

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Meshfree methods have become strong alternatives to conventional numerical methods used in solid mechanics after significant progress in recent years. Radial point interpolation method (RPIM) is a meshfree method based on Galerkin formulation and constructs shape functions which enable easy imposition of essential boundary conditions. This thesis analyses plane elasticity problems using RPIM. A computer code implementing RPIM for the solution of plane elasticity problems is developed. Selected problems are solved and the effect of shape parameters on the accuracy of RPIM with and without polynomial terms added in the interpolation is studied. The optimal shape parameters are determined for plane elasticity problems.

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2

Charlton, Timothy James. "An implicit Generalised Interpolation Material Point Method for large deformation and gradient elasto-plasticity." Thesis, Durham University, 2018. http://etheses.dur.ac.uk/12824/.

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The ability to correctly capture large deformation behaviour in solids is important in many problems in geotechnical engineering such as slope failure or installation of foundations. The Material Point Method (MPM) is a computational method with particular suitability for modelling problems involving large deformations. In the MPM, a domain is modelled using a set of material points at which state variables are stored and tracked. These material points move through a fixed background grid upon which calculations take place with variables being mapped between the material points and the grid. This thesis sets out to develop the MPM as a method with potential for use in geotechnical problems. Problems are encountered with the original MPM when material points cross between grid cells, and one solution to this is the Generalised Interpolation Material Point (GIMP) method, where material points are able to influence nodes beyond the currently occupied grid cell. Most development of the GIMP method has used an explicit approach, however there are a number of advantages of an implicit approach including larger load steps and improved error control. This thesis focuses on the development of a large deformation elasto-plastic implicit GIMP method. A way of calculating the deformation gradient consistent with the MPM is introduced and convergence is demonstrated using this method which has previously been frequently omitted from MPM research. An alternative way of updating material point domains using the stretch tensor is also proposed. The MPM has a number of similarities to the FEM, and it is often suggested that FEM technologies are trivial to use with the MPM. The MPM can encounter localisations caused by shear banding and, to overcome this, a gradient plasticity approach previously implemented for the FEM is investigated with the GIMP method for the first time. The addition of gradient plasticity to the GIMP method introduces a length scale parameter which governs the width of these shear bands and removes the mesh dependency which is encountered with conventional approaches. It is shown that implementation is possible however, there are a number of problems that are present in the combination of the two methods which should not be overlooked in the future.

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3

Kang, Jinghong. "The Computational Kleinman-Newton Method in Solving Nonlinear Nonquadratic Control Problems." Diss., Virginia Tech, 1998. http://hdl.handle.net/10919/30435.

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This thesis deals with non-linear non-quadratic optimal control problems in an autonomous system and a related iterative numerical method, the Kleinman-Newton method, for solving the problem. The thesis proves the local convergence of Kleinman-Newton method using the contraction mapping theorem and then describes how this Kleinman-Newton method may be used to numerically solve for the optimal control and the corresponding solution. In order to show the proof and the related numerical work, it is necessary to review some of earlier work in the beginning of Chapter 1 [Zhang], and to introduce the Kleinman-Newton method at the end of the chapter. In Chapter 2 we will demonstrate the proof. In Chapter 3 we will show the related numerical work and results.
Ph. D.

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4

Leitão, Franklin Delano Cavalcanti. "Métodos sem malha: aplicações do Método de Galerkin sem elementos e do Método de Interpolação de Ponto em casos estruturais." Universidade do Estado do Rio de Janeiro, 2010. http://www.bdtd.uerj.br/tde_busca/arquivo.php?codArquivo=8611.

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Apesar de serem intensamente estudados em muitos países que caminham na vanguarda do conhecimento, os métodos sem malha ainda são pouco explorados pelas universidades brasileiras. De modo a gerar uma maior difusão ou, para a maioria, fazer sua introdução, esta dissertação objetiva efetuar o entendimento dos métodos sem malha baseando-se em aplicações atinentes à mecânica dos sólidos. Para tanto, são apresentados os conceitos primários dos métodos sem malha e o seu desenvolvimento histórico desde sua origem no método smooth particle hydrodynamic até o método da partição da unidade, sua forma mais abrangente. Dentro deste contexto, foi investigada detalhadamente a forma mais tradicional dos métodos sem malha: o método de Galerkin sem elementos, e também um método diferenciado: o método de interpolação de ponto. Assim, por meio de aplicações em análises de barras e chapas em estado plano de tensão, são apresentadas as características, virtudes e deficiências desses métodos em comparação aos métodos tradicionais, como o método dos elementos finitos. É realizado ainda um estudo em uma importante área de aplicação dos métodos sem malha, a mecânica da fratura, buscando compreender como é efetuada a representação computacional da trinca, com especialidade, por meio dos critérios de visibilidade e de difração. Utilizando-se esses critérios e os conceitos da mecânica da fratura, é calculado o fator de intensidade de tensão através do conceito da integral J.
Meshless are certainly very researched in many countries that are in state of art of scientific knowledge. However these methods are still unknown by many brazilian universities. To create more diffusion or, for many people, to introduce them, this work tries to understand the meshless based on solid mechanic applications. So basic concepts of meshless and its historic development are introduced since its origin, with smooth particle hydrodynamic until partition of unity, its more general form. In this context, most traditional form of meshless was investigated deeply: element free Galerkin method and also another different method: point interpolation method. This way characteristics, advantages and disadvantages, comparing to finite elements methods, are introduced by applications in analyses in bars and plates in state of plane stress. This work still researched an important area of meshless application, fracture mechanical, to understand how a crack is computationally represented, particularly, with visibility and diffraction criterions. By these criterions and using fracture mechanical concepts, stress intensity factor is calculated by J-integral concept.

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5

Sendrowski, Janek. "Feigenbaum Scaling." Thesis, Linnéuniversitetet, Institutionen för matematik (MA), 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:lnu:diva-96635.

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In this thesis I hope to provide a clear and concise introduction to Feigenbaum scaling accessible to undergraduate students. This is accompanied by a description of how to obtain numerical results by various means. A more intricate approach drawing from renormalization theory as well as a short consideration of some of the topological properties will also be presented. I was furthermore trying to put great emphasis on diagrams throughout the text to make the contents more comprehensible and intuitive.

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6

Shaterian, Zahra. "Staggered and non-staggered time-domain meshless radial point interpolation method in electromagnetics." Thesis, 2015. http://hdl.handle.net/2440/95232.

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Meshless methods have gained attention recently as a new class of numerical methods for the solution of partial differential equations in various disciplines of computational engineering. This class of methods offers several promising features compared to mesh-based approaches. The principle of domain discretization with arbitrary node distributions allows accurate modeling of complex geometries with fine details. Moreover, an elaborate and time-consuming re-meshing in the grid-based methods can be replaced in meshless counterparts by an adaptive node refinement during the simulation. This can be exploited to enhance solution accuracy or in optimization procedures. In this thesis, the meshless Radial Point Interpolation Method (RPIM) is investigated for application in time-domain computational electromagnetics. The numerical algorithm is based on a combination of locally defined radial and polynomial basis functions and yields a highly accurate local interpolation of field values and associated derivatives based on the values at close neighboring positions. These interpolated partial derivatives are used to solve the partial differential equations. The thesis is firstly focused on the staggered meshless RPIM. The classical implementation of the staggered meshless RPIM in electromagnetics using the first-order Maxwell’s curl equations is described and the update equations for the staggered electric and magnetic fields are shown. To enhance the capability of the algorithm, a novel implementation of the Uniaxial Perfectly Matched Layer (UPML) is introduced. It is shown however that UPML has intrinsically a long-time instability. Therefore, to avoid this instability two loss terms are introduced, which are added to the update equations in the UPML region after almost all the energy from the computational domain is absorbed. Various capabilities of the meshless method are then validated through different numerical examples using staggered node arrangements in the staggered meshless RPIM. However, the generation of a dual node distribution can be computationally costly and restricts the freedom of node positions, which might reduce the potential advantages of the scheme. To overcome this challenge, the thesis next proposes a novel non-staggered algorithm for the meshless RPIM based on a magnetic vector potential technique. In this method instead of solving Maxwell’s curl equations for the electric and magnetic fields, the wave equation for the magnetic vector potential is solved. Therefore, a single set of nodes can be used to discretize the computational domain. Importantly in the proposed implementation, solving the second-order vector potential wave equation intrinsically enforces the divergence-free property of the electric and magnetic fields and the computational effort associated with the generation of a dual node distribution is avoided. In this part of the thesis, a hybrid algorithm is further proposed to implement staggered perfectly matched layers in the non-staggered RPIM framework. The properties of the proposed non-staggered RPIM are evaluated through several numerical examples both in 2D and 3D implementations. In the last part of the thesis, the staggered and non-staggered implementations of meshless RPIM are directly compared in terms of efficiency and accuracy. It is shown that the non-staggered meshless RPIM not only bypasses the requirement of the dual node distribution, but also suppresses the spurious solutions observed in the staggered implementation. The results of this research show the capability of meshless RPIM for being used efficiently in time-domain computational electromagnetics.
Thesis (Ph.D.) -- University of Adelaide, School of Electrical and Electronic Engineering, 2015

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7

Azevedo, José Manuel Cruz. "Fracture mechanics using the natural neighbour radial point interpolation method." Dissertação de mestrado, 2013. http://hdl.handle.net/10216/72564.

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8

Moreira, Susana Fernandes. "Elastoplastic analysis using the Natural Neighbour Radial Point Interpolation Method." Master's thesis, 2013. https://repositorio-aberto.up.pt/handle/10216/100302.

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9

Azevedo, José Manuel Cruz. "Fracture mechanics using the Natural Neighbour Radial Point Interpolation Method." Master's thesis, 2013. https://hdl.handle.net/10216/96261.

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10

Moreira, Susana Fernandes. "Elastoplastic analysis using the Natural Neighbour Radial Point Interpolation Method." Dissertação, 2013. https://repositorio-aberto.up.pt/handle/10216/100302.

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11

Ramalho, Luís Daniel Costa. "Modelling Crack Propagation Using the Finite Element Method and Radial Point Interpolation Meshless Methods." Master's thesis, 2018. https://repositorio-aberto.up.pt/handle/10216/114145.

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12

Ramalho, Luís Daniel Costa. "Modelling Crack Propagation Using the Finite Element Method and Radial Point Interpolation Meshless Methods." Dissertação, 2018. https://repositorio-aberto.up.pt/handle/10216/114145.

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13

Belinha, Jorge Américo Oliveira Pinto. "The natural neighbour radial point interpolation method : solid mechanics and mechanobiology applications." Doctoral thesis, 2010. http://hdl.handle.net/10216/57990.

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14

Belinha, Jorge Américo Oliveira Pinto. "The natural neighbour radial point interpolation method : solid mechanics and mechanobiology applications." Tese, 2010. http://hdl.handle.net/10216/57990.

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15

Chi-PeiTsai and 蔡季培. "Simulation of fracture analysis in the plate by meshless radial point interpolation method." Thesis, 2014. http://ndltd.ncl.edu.tw/handle/76112000384578667865.

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碩士
國立成功大學
機械工程學系
102
This thesis presents a meshless radial point interpolation method (RPIM) model for simulation of two dimensional displacement and stress of fracture analysis in the plate. As a kind of newly developed numerical methods, meshfree method can overcome discontinuous material problems which trouble the conventional finite element method. As a kind of meshfree method, radial basis function received many researchers’ interest due to its characteristics of rapid convergence, simple expression, shape function are infinitely differentiable and continuous,etc. In order to verify the model, the displacement and stress condition of cantilever beam in force, results is well-agreement of previously literature. And discuss the impact of different shape functions, different nodes by this method. Then this paper simulates a beam with notch, understand the discontinuous material and different depths impact on the linear elastic structure , making it through different forms of notch has very good results in RPIM. Finally, the effect of the crack on the structure by notch and visibility criterion was present. Different distribution of displacement and stress can be discussed in different forms of cracks, and the different depth of crack also had well-agreement by RPIM.

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16

Duarte, Henrique Manuel Sousa. "The material non linear analysis of 2D strutures using a radial point interpolation method." Master's thesis, 2014. https://repositorio-aberto.up.pt/handle/10216/84114.

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17

Costa, Rui Orlando Silva Sampaio da. "The Extension of a Radial Point Interpolation Meshless Method to the Viscoplastic Extrusion process." Master's thesis, 2018. https://hdl.handle.net/10216/113520.

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18

Costa, Rui Orlando Silva Sampaio da. "The Extension of a Radial Point Interpolation Meshless Method to the Viscoplastic Extrusion process." Dissertação, 2018. https://hdl.handle.net/10216/113520.

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19

Duarte, Henrique Manuel Sousa. "The material non linear analysis of 2D strutures using a radial point interpolation method." Dissertação, 2014. https://repositorio-aberto.up.pt/handle/10216/84114.

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20

Farahani, Behzad Vasheghani. "The radial point interpolation meshless method extended to axisymmetric plates and non-linear continuum damage mechanics." Master's thesis, 2015. https://repositorio-aberto.up.pt/handle/10216/90296.

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21

Farahani, Behzad Vasheghani. "The radial point interpolation meshless method extended to axisymmetric plates and non-linear continuum damage mechanics." Dissertação, 2015. https://repositorio-aberto.up.pt/handle/10216/90296.

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22

Pires, Luís Filipe Gonçalves. "Propagação de fenda utilizando um método sem malha." Master's thesis, 2012. http://hdl.handle.net/10216/68137.

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23

Pires, Luís Filipe Gonçalves. "Propagação de fenda utilizando um método sem malha." Dissertação, 2012. http://hdl.handle.net/10216/68137.

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24

Ma, Jin. "Multiscale simulation using the generalized interpolation material point method, discreet dislocations and molecular dynamics." 2006. http://digital.library.okstate.edu/etd/umi-okstate-1823.pdf.

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