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A novel nodal integration technique for meshfree methods based on the cartesian transformation approach in the analysis of curved shells

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ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS 2024年 163卷 69-83页

作者： Truong, Thien Tich Nguyen, Nha Thanh Nguyen, Dinh Kien Lo, Vay Siu Ho Chi Minh City Univ Technol HCMUT Fac Appl Sci Dept Engn Mech 268 Ly Thuong Kiet StDist 10 Ho Chi Minh City Vietnam Vietnam Natl Univ Ho Chi Minh City Linh Trung Ward Ho Chi Minh City Vietnam VAST Inst Mech 18 Hoang Quoc Viet Hanoi Vietnam

In this paper, a novel nodal integration technique for meshfree methods is introduced. This technique is based on the idea of the cartesian transformation method, which prevents the presence of background cells during the numerical integration process. The Gauss-Lobatto quadrature is used instead of the conventional Gaussian quadrature to create the integration points so that the integration points coincide with the field nodes. This development gave rise to an innovative nodal integration method that eliminates the necessity for generating integration cells, thus advancing further toward a genuinely meshfree approach. The meshfree method chosen in this study is the radial point interpolation method due to the satisfaction of the Kronecker delta property. The curved shell is formulated by the first-order shear deformation theory (FSDT). The static and free vibration analyses of different geometry curved shells are conducted. Through several numerical examples, the accuracy and efficiency of the proposed technique are demonstrated and discussed. It is found that the current technique has better performance than the existing numerical integration techniques used in meshfree method. Furthermore, this new nodal integration technique also shows the ability to mitigate the shear-locking phenomenon when analyzing the problem of thin shells using the FSDT formulation.

关键词： Nodal integration cartesian transformation method Meshfree method Curved shells

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A novel meshfree radial point interpolation method with discrete shear gap for nonlinear static analysis of functionally graded plates

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ENGINEERING WITH COMPUTERS 2023年第4期39卷 2989-3009页

作者： Truong, Thien T. Lo, Vay S. Nguyen, Minh N. Nguyen, Nha T. Nguyen, Kien D. Ho Chi Minh City Univ Technol Fac Appl Sci Dept Engn Mech 268 Ly Thuong Kiet StDist 10 Ho Chi Minh City Vietnam Vietnam Natl Univ Ho Chi Minh City Ho Chi Minh City Vietnam VAST Inst Mech 18 Hoang Quoc Viet Hanoi Vietnam

In this paper, the discrete shear gap (DSG) is for the first time incorporated into the meshfree radial point interpolation method (RPIM) for nonlinear static analysis of functionally graded plates based on Reissner-Mindlin theory. The technique of DSG, originally developed for finite element analysis during the last decades, is re-formulated to be adopted into a meshfree analysis to treat the well-known shear locking issue and to improve accuracy. As one of the rare meshfree scheme that possesses Kronecker delta property, the RPIM allows direct imposition of boundary conditions. Numerical integration is conducted by the cartesian transformation method (CTM), which enables the possibility to avoid the creation of background cells during numerical integration, making one step further towards a truly meshfree approach, in the sense that there is no discretization of problem domain into sub-domains either in the form of elements or integration cells. For non-linear analysis, the iterative Newton-Raphson scheme is employed. Via various numerical examples, the accuracy and efficiency of the proposed approach (i.e. RPIM with DSG) is demonstrated and discussed. It is found that the DSG has better performance than other existing techniques used in meshfree RPIM analysis of Reissner-Mindlin plates.

关键词： Meshfree RPIM analysis Functionally graded plates Reissner-Mindlin theory cartesian transformation method Discrete shear gap

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A new time-domain boundary element formulation for generalized models of viscoelasticity

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ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS 2023年第1期150卷 30-43页

作者： Akay, Ahmet Arda Gurses, Ercan Goktepe, Serdar Middle East Tech Univ Dept Aerosp Engn Dumlupinar Bulvari 1 TR-06800 Ankara Turkiye Middle East Tech Univ Dept Civil Engn Dumlupinar Bulvari 1 TR-06800 Ankara Turkiye

The contribution is concerned with the novel algorithmic formulation for generalized models of viscoelasticity under quasi-static conditions within the framework of the boundary element method (BEM). The proposed update algorithm is constructed for a generic rheological model of linear viscoelasticity that can either be straightforwardly simplified to recover the basic Kelvin and Maxwell models or readily furthered towards the generalized models of viscoelasticity through the serial or parallel extensions. In contrast to the scarce existing rate formulations of inelasticity developed within BEM, the put forward non-iterative formulation exploits the hybrid semi-implicit update of strain-like kinematic history variables. The challenge arising from the indispensable domain integrals is overcome through the mesh-free cartesian transformation method (CTM), complemented by the radial point integration (RPIM) technique. The excellent performance of the proposed approach is demonstrated in comparison with the corresponding analytical and finite element results for boundary-value problems with uniform and non-uniform strain fields under different representative modes and types of loading.

关键词： Boundary element method Linear viscoelasticity Meshless domain integration cartesian transformation method Radial point interpolation method Semi-implicit time integration

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Development of an adaptive CTM-RPIM method for modeling large deformation problems in geotechnical engineering

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ACTA GEOTECHNICA 2022年第6期17卷 2059-2077页

作者： Li, Jianguo Wang, Bin Jiang, Quan He, Benguo Zhang, Xue Vardon, Philip J. Chinese Acad Sci Inst Rock & Soil Mech State Key Lab Geomech & Geotech Engn Wuhan Peoples R China Univ Chinese Acad Sci Beijing Peoples R China Northeastern Univ Minist Educ Safe Min Deep Met Mines Key Lab Shenyang Peoples R China Univ Liverpool Dept Civil Engn & Ind Design Liverpool Merseyside England Delft Univ Technol Geoengn Sect Delft Netherlands

In this paper, a meshfree method called adaptive CTM-RPIM is developed to model geotechnical problems with large deformation. The developed adaptive CTM-RPIM is a combination of the cartesian transformation method (CTM), the radial point interpolation method (RPIM) and the alpha shape method. To reduce the requirement for meshes, the CTM is adopted to transform domain integrals into line integrals, and the RPIM is applied to construct interpolation functions. The alpha shape method, which is capable of capturing severe boundary evolution due to large deformations, is then introduced into the CTM-RPIM to form the adaptive CTM-RPIM. The accuracy of CTM-RPIM is first verified by considering a cantilever beam under small deformation, where the influence of key parameters on the simulation results is explored. Afterward, the ability of the adaptive CTM-RPIM to handle large deformation problems is demonstrated by simulating cantilever beams with large deformations for which analytical solutions are available. Finally, the ability of the proposed method to model the geotechnical large deformations is illustrated from both quasi-static and dynamic aspects, where a slope failure problem and a footing bearing capacity problem are modeled to evaluate the stability of geotechnical structures;and a 2-D soil collapse experiment using small aluminum bars is simulated to show the method capability in describing the soil flows. These benchmark examples demonstrate that the adaptive CTM-RPIM is a numerical method with broad application prospects for modeling large deformation problems in geotechnical engineering.

关键词： Alpha shape method cartesian transformation method Geotechnical engineering Large deformation Radial point interpolation method

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A New BEM for Fractional Nonlinear Generalized Porothermoelastic Wave Propagation Problems

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Computers, Materials & Continua 2021年第7期68卷 59-76页

作者： Mohamed Abdelsabour Fahmy Department of Mathematics Jamoum University CollegeUmm Al-Qura UniversityAlshohdaa25371JamoumSaudi Arabia Department of Basic Sciences Faculty of Computers and InformaticsSuez Canal UniversityNew CampusIsmailia41522Egypt

The main purpose of the current article is to develop a novel boundary element model for solving fractional-order nonlinear generalized porothermoelastic wave propagation problems in the context of temperaturedependent functionally graded anisotropic(FGA)*** system of governing equations of the considered problem is extremely very difficult or impossible to solve analytically due to nonlinearity,fractional order diffusion and strongly anisotropic mechanical and physical properties of considered porous ***,an efficient boundary element method(BEM)has been proposed to overcome this difficulty,where,the nonlinear terms were treated using the Kirchhoff transformation and the domain integrals were treated using the cartesian transformation method(CTM).The generalized modified shift-splitting(GMSS)iteration method was used to solve the linear systems resulting from BEM,also,GMSS reduces the iterations number and CPU execution time of *** numerical findings show the effects of fractional order parameter,anisotropy and functionally graded material on the nonlinear porothermoelastic stress *** numerical outcomes are in very good agreement with those from existing literature and demonstrate the validity and reliability of the proposed methodology.

关键词： Boundary element method fractional-order nonlinear generalized porothermoelasticity wave propagation functionally graded anisotropic structures cartesian transformation method

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A new boundary element algorithm for modeling and simulation of nonlinear thermal stresses in micropolar FGA composites with temperature-dependent properties

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ADVANCED MODELING AND SIMULATION IN ENGINEERING SCIENCES 2021年第1期8卷 1-23页

作者： Fahmy, Mohamed Abdelsabour Jamoum Univ Coll Umm Al Qura Univ Mecca 25371 Saudi Arabia Suez Canal Univ Fac Comp & Informat New Campus4-5 KmRing Rd Ismailia 41522 Egypt

The main aim of this article is to develop a new boundary element method (BEM) algorithm to model and simulate the nonlinear thermal stresses problems in micropolar functionally graded anisotropic (FGA) composites with temperature-dependent properties. Some inside points are chosen to treat the nonlinear terms and domain integrals. An integral formulation which is based on the use of Kirchhoff transformation is firstly used to simplify the transient heat conduction governing equation. Then, the residual nonlinear terms are carried out within the current formulation. The domain integrals can be effectively treated by applying the cartesian transformation method (CTM). In the proposed BEM technique, the nonlinear temperature is computed on the boundary and some inside domain integral. Then, nonlinear displacement can be calculated at each time step. With the calculated temperature and displacement distributions, we can obtain the values of nonlinear thermal stresses. The efficiency of our proposed methodology has been improved by using the communication-avoiding versions of the Arnoldi (CA-Arnoldi) preconditioner for solving the resulting linear systems arising from the BEM to reduce the iterations number and computation time. The numerical outcomes establish the influence of temperature-dependent properties on the nonlinear temperature distribution, and investigate the effect of the functionally graded parameter on the nonlinear displacements and thermal stresses, through the micropolar FGA composites with temperature-dependent properties. These numerical outcomes also confirm the validity, precision and effectiveness of the proposed modeling and simulation methodology.

关键词： Boundary element method Modeling algorithm Nonlinear thermal stresses Micropolar thermoelasticity Functionally graded anisotropic composites cartesian transformation method

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Meshfree thermomechanical crack growth simulations with new numerical integration scheme

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ENGINEERING FRACTURE MECHANICS 2020年 235卷 107121-107121页

作者： Nha Thanh Nguyen Tinh Quoc Bui Minh Ngoc Nguyen Thien Tich Truong Ho Chi Minh City Univ Technol VNU HCM Fac Sci Appl Dept Engn Mech Ho Chi Minh City Vietnam Tokyo Inst Technol Dept Civil & Environm Engn Meguro Ku 2-12-1-W8-22 Ookayama Tokyo 1528552 Japan

This paper presents for the first time an improved meshfree particle method without the need for background cells in terms of numerical integration for thermal-mechanical crack growth analysis. In this work, both adiabatic and isothermal crack surfaces are considered. Asymptotic solutions-based enriched functions are incorporated into the approximation scheme to mathematically capture jump across crack surfaces of both the temperature and displacements, as well as the singularities of heat fluxes and stresses in the vicinity of crack tip. Once the stress intensity factors (SIFs) are evaluated, the direction of crack growth can be determined. The meshfree analysis is based on radial point interpolation method (RPIM), in which cartesian transformation method (CTM) is adopted for numerical integration, instead of the conventional Gaussian quadrature. The utilization of Gaussian scheme requires background cells in shape of quadrilaterals or triangles. In contrast, the CTM is advantageous in the manner that the background cells are no longer required, leading to truly meshfree formulation. The novel contribution of the current work is the extension of CTM scheme in which the integration domain is updated according to crack growth. The crack surfaces are viewed as part of the boundaries of the problem domain. Therefore, it is guaranteed that no discontinuities exist within the domain. The accuracy of the proposed approach is demonstrated by comparison of computed results with reference ones from analytical solution, and other existing numerical methods.

关键词： Fracture Meshfree Thermo-elasticity Numerical integration Crack growth cartesian transformation method

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Evaluation of fracture parameters in cracked plates using an extended meshfree method

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ENGINEERING FRACTURE MECHANICS 2021年 247卷 107671-107671页

作者： Thien Tich Truong Vay Siu Lo Minh Ngoc Nguyen Nha Thanh Nguyen Dinh Kien Nguyen Ho Chi Minh City Univ Technol Fac Appl Sci Dept Engn Mech 268 Ly Thuong Kiet StDist 10 Ho Chi Minh City Vietnam Vietnam Natl Univ Ho Chi Minh City Linh Trung Ward Ho Chi Minh City Vietnam VAST Inst Mech 18 Hoang Quoc Viet Hanoi Vietnam

In this paper, an extended meshfree method approach is developed for numerical analysis of cracked plates using the First order Shear Deformation Theory ? FSDT. Extrinsic enriched functions are employed to capture the jump in deflection and rotation fields, as well as the stress singularity in the vicinity of crack tip. Meshfree approximation of field variables is done by the Radial Point Interpolation method, which possesses the desirable Kronecker-delta property, unlike many other meshfree methods. Numerical integration is conducted by the cartesian transformation method (CTM), which turns a domain integration into a 1D integration and a boundary integration. As alternative to conventional Gaussian Quadrature (GQ), CTM is advantageous in the context of meshfree analysis, such that background cells are no longer required, forming a truly meshfree formulation. Furthermore, crack surfaces are viewed as part of the domain boundaries and thus, it is guaranteed that no discontinuities exist within the integration domain. The accuracy of the present approach is demonstrated by various numerical examples, in which Stress Resultant Intensity Factors (SRIFs) are evaluated. Obtained numerical results are compared with reference solutions derived from analytical, experimental and other existing numerical methods. It is also exhibited that CTM is more suitable to the meshfree context than GQ.

关键词： Fracture Meshfree analysis Bending plate FSDT cartesian transformation method

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A comparative study of three domain-integral evaluation techniques in the boundary-domain integral equation method for transient thermoelastic crack analysis in FGMs

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CMES-COMPUTER MODELING IN ENGINEERING & SCIENCES 2013年第6期92卷 595-614页

作者： Ekhlakov, A. V. Khay, O. M. Zhang, Ch. Gao, X. W. Sladek, J. Sladek, V. Univ Siegen Dept Civil Engn D-57068 Siegen Germany Univ Appl Sci Fac Architecture & Civil Engn D-65197 Wiesbaden Germany Pidstryhach Inst Appl Problems Mech & Math NASU UA-79060 Lvov Ukraine Dalian Univ Technol Fac Vehicle Engn & Mech Dalian 116024 Peoples R China Slovak Acad Sci Inst Construct & Architecture Bratislava 84503 Slovakia

A boundary-domain integral equation method is applied to the transient thermoelastic crack analysis in functionally graded materials. Fundamental solutions for homogeneous, isotropic and linear elastic materials are used to derive the boundary-domain integral equations. The radial integration method, the cartesian transformation method and the cell-integration method are applied for the evaluation of the arising domain-integrals. Numerical results for dynamic stress intensity factors obtained by the three approaches are presented, compared and discussed to show the accuracy and the efficiency of the domain-integral evaluation techniques.

关键词： Radial integration method cartesian transformation method cell-integration method dynamic stress intensity factors functionally graded materials

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