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A unified approach to the mathematical analysis of generalized RKPM, gradient RKPM, and GMLS
, Article Computer Methods in Applied Mechanics and Engineering ; Volume 200, Issue 5-8 , January , 2011 , Pages 540-576 ; 00457825 (ISSN) ; Shodja, H. M ; Khezri, M ; Sharif University of Technology
2011
Abstract
It is well-known that the conventional reproducing kernel particle method (RKPM) is unfavorable when dealing with the derivative type essential boundary conditions [1-3]. To remedy this issue a group of meshless methods in which the derivatives of a function can be incorporated in the formulation of the corresponding interpolation operator will be discussed. Formulation of generalized moving least squares (GMLS) on a domain and GMLS on a finite set of points will be presented. The generalized RKPM will be introduced as the discretized form of GMLS on a domain. Another method that helps to deal with derivative type essential boundary conditions is the gradient RKPM which incorporates the...
Determination of the Plastic Zone at the Tip of a Crack in Pressure-Sensitive Materials Using RKPM
, M.Sc. Thesis Sharif University of Technology ; Mohammadi Shoja, Hossein (Supervisor) ; Jahanshahi, Mohsen (Supervisor)
Abstract
This project presents an outline of the crack tip stress fields in the presence of a plastic enclave around a growing fatigue crack using RKPM and Drucker-Prager criterion for pressure sensitive materials such as concrete and rock. Two distinguished features of RKPM are the arbitrarily high order smoothness and the interpolation property of the shape function which has kronecker delta property at the associated nodes. This method has proved to handle extreme material deformation and moving discontinuities. For the frictional materials such as rock in geotechnical engineering, a non-associated or associated Drucker- Prager plasticity model is appropriate for modeling its constitutive...
Dynamic response of euler-Bernoulli, Timoshenko and higher-Order beams under a moving mass via RKPM
, Article 7th European Conference on Structural Dynamics, EURODYN 2008, 7 July 2008 through 9 July 2008 ; 2008 ; 9780854328826 (ISBN) ; Kiani, K ; Mehri, B ; Sharif University of Technology
University of Southampton, Institute of Sound Vibration and Research
2008
Abstract
Discrete motion equations of an Euler-Bernoulli, Timoshenko and higher-order beams under a moving mass are derived for different boundary conditions. To this end, the reproducing kernel particle method (RKPM) has been utilized for spatial discretization, beside the extension of Newmark-β method for time discretization of the beams motion equations. The effects of significant parameters such as the beam's slenderness and velocity of the moving mass on the maximum deflection and bending moment of different beams are studied in some details. The results indicate the existence of a critical beam's slenderness mostly as a function of beam's boundary conditions, in which for slenderness lower than...
A remedy to gradient type constraint dilemma encountered in RKPM
, Article Advances in Engineering Software ; Volume 38, Issue 4 , 2007 , Pages 229-243 ; 09659978 (ISSN) ; Hashemian, A ; Sharif University of Technology
Elsevier Ltd
2007
Abstract
A major disadvantage of conventional meshless methods as compared to finite element method (FEM) is their weak performance in dealing with constraints. To overcome this difficulty, the penalty and Lagrange multiplier methods have been proposed in the literature. In the penalty method, constraints cannot be enforced exactly. On the other hand, the method of Lagrange multiplier leads to an ill-conditioned matrix which is not positive definite. The aim of this paper is to boost the effectiveness of the conventional reproducing kernel particle method (RKPM) in handling those types of constraints which specify the field variable and its gradient(s) conveniently. Insertion of the gradient term(s),...
Analysis of a Lamellar Inhomogeneity Via Repordusing Kernel Particle Method
, M.Sc. Thesis Sharif University of Technology ; Mohammadi Shodja, Hossein (Supervisor)
Abstract
Nowadays, the excellent technological applications of composites have attracted the attentions of industry and numerous scientists. They are advantageous for their high tensile modulus, strength, and promising electrical and thermal properties. In applying the approach of lamellar inhomogeneity to real composites, the micro-geometries of the reinforcement must be considered such that they can be approximated as limiting case of an ellipsoid. In vapor grown carbon nanofiber, the fiber may have a diameter of about 150nm and length of 10-20 µm [1]. The modulus of carbon nanofiber is normally in the range of 100-600 GPa and sometimes even higher, whereas the modulus of some polymers is usually...
Buckling Analysis of Nano-Plates in the Context of Modified Couple Stress Theory Using RKPM
, M.Sc. Thesis Sharif University of Technology ; Mohammadi Shoja, Hossein (Supervisor)
Abstract
In this research, a new Kirchhoff plate model based on the modified couple stress theory has been utilized to derive the corresponding closed-form expression for the buckling load. Moreover, a numerical mesh-less method, Reproducing Kernel Particle Method (RKPM), in combination with Corrected Collocation Method (CCM) has been employed to model the nano-plate and calculate its buckling load in the framework of the modified couple stress theory. To this end, two kinds of nano-plates have been modeled, the square nano-plates with all edges simply supported 1) in the presence of the nano-void and 2) without the nano-void. It should be noted that the analytical and numerical solutions for the...
Augmented RKPM Modeling of a Glide Edge Dislocation Near a Grain Boundary in the Framework of Surface/Interface Elasticity
, M.Sc. Thesis Sharif University of Technology ; Mohammadi Shoja, Hossein (Supervisor)
Abstract
Traditional continuum theory of elasticity becomes remarkably inaccurate in the vicinity of singularities, and when the size eect is of concern. For example in the study of ultra-small objects and ultra-thin lms, near defects, near point of application of a concentrated load and as such, the classical solutions are not reliable. This work focuses on determination of the elastic elds of an edge dislocation near the grain boundary of two perfectly bonded nano-size crystals. It is proposed to study this problem in the context of surface/interface elasticity, and incorporate the eect of the grain boundary on the elastic elds. In contrast to the surface/interface elasticity theory, traditional...
Elastic Field of an Anticrack Via Reproducing Kernel Particle Method
, M.Sc. Thesis Sharif University of Technology ; Mohammadi Shodja, Hossein (Supervisor)
Abstract
Meshless Methods using kernel approximation like Reproducing Kernel Particle Method (RKPM) are methods for solving partial differential equations that require only nodal data and a description of the geometry without requiring element connectivity data and mesh producing. An innovative method of nonplanar material partitioning method (NMPM) with implementation of RKPM is employed to calculate the stress intensity factor (SIF) at the tip of an anticrack sited in an isotropic plate under a remote applied loading. Numerical examples in comparison with the exact closed form expressions show that accurate SIF for mode I can be obtained.
Study of Size Effect via Strain-gradient Elasticity Based RKPM in Nano-Structures
, M.Sc. Thesis Sharif University of Technology ; Mohammadi Shoja, Hossein (Supervisor)
Abstract
In this thesis one of the mesh-free methods called RKPM is employed to solve the differential equations of strain-gradient elasticity. To this end the corresponding weak form is laid down. Subsequently the relevant stiffness-matrix is obtained by discretization of the weak form. To be sure about the accuracy of the relations, the problem of a plate weakened by a hole under uniform far-field tension, for which the exact solution is available in the literature, is solved. The obtained numerical result is in good agreement with the solution of Eshel and Rosenfeld. Afterwards, a plate containing a crack of finite length subjected to uniform far-field tension (mode I) is considered. This problem...
Reproducing Kernel particle method in plasticity of pressure-sensitive material with reference to powder forming process
, Article Computational Mechanics ; Volume 39, Issue 3 , 2007 , Pages 247-270 ; 01787675 (ISSN) ; Samimi, M ; Azami, A. R ; Sharif University of Technology
Springer Verlag
2007
Abstract
In this paper, an application of the reproducing kernel particle method (RKPM) is presented in plasticity behavior of pressure-sensitive material. The RKPM technique is implemented in large deformation analysis of powder compaction process. The RKPM shape function and its derivatives are constructed by imposing the consistency conditions. The essential boundary conditions are enforced by the use of the penalty approach. The support of the RKPM shape function covers the same set of particles during powder compaction, hence no instability is encountered in the large deformation computation. A double-surface plasticity model is developed in numerical simulation of pressure-sensitive material....
Application of rkpm in numerical simulation of powder forming processes using cap plasticity model
, Article 8th International Conference on Computational Plasticity: Fundamentals and Applications, COMPLAS VIII, Barcelona, 5 September 2005 through 7 September 2005 ; Issue PART 2 , 2005 , Pages 966-969 ; 849599979X (ISBN); 9788495999795 (ISBN) ; Khoei, A. R ; Sharif University of Technology
2005
Abstract
In this paper, an application of the Reproducing Kernel Particle Method is presented in numerical simulation of powder forming processes using a cap plasticity model. A double-surface cap plasticity is developed within the framework of large deformation analysis in order to predict the non-uniform relative density distribution during powder die pressing. The RKPM technique is employed in the analysis of 2D compaction simulation. Numerical examples are presented to illustrate the applicability of the algorithm in modelling of powder forming processes
Analysis of Cohesive Crack Via Reproducing Kernel Particle Method (RKPM)
, M.Sc. Thesis Sharif University of Technology ; Shodja, Hossain (Supervisor)
Abstract
The aim of this work is to study a cohesive crack in an elastic solid with meshless method. The procedure uses Reproducing Kernel Particle Method (RKPM) formulation in conjunction with Penalty method for implementing all constraints, including the Essential Boundary Conditions (EBCs) and the constraints related to cohesive crack. Meanwhile subdomain technique is employed to diminish the compiling process to facilitate one. Study of Stress Intensity Factor (SIF) at the tip of the cohesive crack has also been dealt with particular interest
Numerical Modeling of a Nano Crack in Fcc Solids Using RKPM Based Dipolar Gradient Elasticity
, M.Sc. Thesis Sharif University of Technology ; Mohammadi Shodja, Hosain (Supervisor)
Abstract
In many structures, crack creation is one of the most significant fracture mechanisms. To predict these fracture mechanisms accurate numerical modeling is necssary. Finite Element Method (FEM) is one of the substantial methods in analysis of numerical fracture problems in recent past decades. But, this method has difficulties in remeshing of elements in each step of calculation in fracture mechanics or large deformation analysis. Therefore, the theory was defined that, without using elements, just with setting of characteristics nodes in geometry of problem, the differential equations can be solved. These methods are called Meshfree or Meshless methods. RKPM is a new meshfree method for...
Elastoplastic Analysis of Planar Cracks Under Tension Using RKPM
,
M.Sc. Thesis
Sharif University of Technology
;
Mohammadi Shodja, Hossein
(Supervisor)
Abstract
During recent years, many researches on meshfree methods to solve differential equations and crack problem have been accomplished, and acceptable results have been obtained. One of these methods which is widely used in fracture mechanics specially in problems including crack is RKPM (reproducing kernel particle method). RKPM is one of the modern numerical methods in solving differential equations that has been lately introduced and developed. In this method, the genuine response of the system is replaced with a good approximation of the real response called ‘Reproduced Function’. The formulation of this method obviates the need for discretizing the domain by meshing with elements. In this...
Numerical Modeling of Two Interacting Circular Holes Using a Gradient Elasticity Based Meshless Method
, M.Sc. Thesis Sharif University of Technology ; Mohammadi Shoja, Hossain (Supervisor)
Abstract
A theory of gradient elasticity is used and numerically implemented by a meshless method that is called reproducing kernel particle method (RKPM) to model size effects. Some of the problems are modeled under the consideration of gradient elasticity for the first time and all of them are also modeled with classical elasticity to compare with gradient elasticity. First of all, the RKPM formulation and computing the amount of shape functions and requisite derivatives will be explained with details and a mathematical innovation that will decrease the computational cost seriously proposed for the first time. Several 1D and 2D shape functions with first and second derivatives that are resulted...
, M.Sc. Thesis Sharif University of Technology ; Mohammadi Shodja, Hossien (Supervisor)
Abstract
The present study aims at determining the elastic fields of ultra-small flaws and defects. These defects are often introduced undesirably in elastic solids during fabrication and their sizes are normally in the order of couple of nano-meters. In this work, the elastic fields around a circular nano-void subjected to a uniform farfield uniaxial tension, also the elastic fields of a nano-sized mode I crack under remote uniform loading are studied. In this paper the strain gradient theory developed by Mindlin and co-workers in 1960s is employed. According to this theory, the strain energy density assumes the form of a positive-definite function of the strain components and their first gradient....
Determination of the Two-Dimensional Plastic Zone Size and SIF at the Crack Tip Using RKPM
,
M.Sc. Thesis
Sharif University of Technology
;
Mohammadi Shodja, Hossein
(Supervisor)
Abstract
It is proposed to obtain the mode I plastic zone size and shape at the crack-tip in a work-hardening material using reproducing kernel particle method (RKPM). RKPM is a meshless technology which has proven very useful for solving problems of fracture mechanics. Ramberg-Osgood stress-strain relation is assumed. In this project the crack-tip stress intensity factor (SIF) before and after formation of the plastic zone will be examined. To impose the essential boundary conditions, penalty method is used. To construct the shape functions in the vicinity of the crack and crack-tip, both the diffraction and visibility methods are employed. The effects of different dilation parameters on SIF under...
Determination of the Elastic Fields of Eliptic Inhomogeneities and Inclusions in Anti-Plane Couple Stress Elasticity Using RKPM
, M.Sc. Thesis Sharif University of Technology ; Mohammadi Shodja,Hossain (Supervisor)
Abstract
In this research, circular and elliptic inhomogeneities are modeled using a numerical meshless method named RKPM. A newly developed accurate and simple method called augmented corrected collocation method, which was previously applied in order to model material discontinuities in the framework of classical continuum theory, is used in combination with the penalty method, considering couple stress elasticity and in micro or nano scales for the first time, where the classical continuum theory has certain shortcomings in predicting the behavior of materials. Simulating nano-composites subjected to anti-plane stresses and comparing the analytical and numerical results show that the augmented...
RKPM with Etxtended Augmented Corrected Collocation Method for Treatment of Lamellar Inhomogeneitie
, M.Sc. Thesis Sharif University of Technology ; Mohammadi Shoja, Hossein (Supervisor)
Abstract
An accurate numerical methodology for capturing the field quantities a center lamellar inhomogeneity within the interface of two different phases of a bimaterial rectangular plate subjected to non-uniform tensile stress, in the context of reproducing kernel particle method (RKPM), is of particular interest. For this purpose the innovative numerical technique, so-called extended augmented corrected collocation method is introduced; this technique is an extension of the augmented corrected collocation method used for imposing continuity condition of the displacement at the interface. The robustness of this methodology is shown by solving problems of material discontinuities, namely plates...
Vibration Analysis of FGM Beam Using RKPM Meshlesh Method
, M.Sc. Thesis Sharif University of Technology ; Ahmadian, Mohammad Taghi (Supervisor)
Abstract
Due to special characteristics, nowadays functionally graded materials are of great interest of researchers. Continuous change of properties in these materials,decreases undesirable phenomena such as stresscon centration. On the other hand knowing vibration parameters of structures such as natural frequencies, to avoid damage, is important. So far, many researches have been devoted to vibration analysis of structures, such as beams.In this dissertation, free vibration analysis of FGM beams, are investigated, using RKPM, a meshlesh method. The system of equations of motion is derived using Lagrange’s method under the assumption of Euler-Bernoulli beam theory. Buckling analysis of FGM beams...