A high-performance boundary element method and its applications in engineering

As a semi-numerical and semi-analytical method, owing to the inherent advantage, of boundary-only discretisation, the boundary element method (BEM) has been widely applied to problems with complicated geometries, stress concentration problems, infinite domain problems, and many others. However, domain integrals and non-symmetrical and dense matrix systems are two obstacles for BEM which have hindered the its further development and application. This thesis is aimed at proposing a high-performance BEM to tackle the above two drawbacks and broaden the application scope of BEM. In this thesis, a detailed introduction to the traditional BEM is given and several popular algorithms are introduced or proposed to enhance the performance of BEM. Numerical examples in heat conduction analysis, thermoelastic analysis and thermoelastic fracture problems are performed to assess the efficiency and correction of the algorithms. In addition, necessary theoretical derivations are embraced for establishing novel boundary integral equations (BIEs) for specific engineering problems. The following three parts are the main content of this thesis. (1) The first part (Part II consisting of two chapters) is aimed at heat conduction analysis by BEM. The coefficient matrix of equations formed by BEM in solving problems is fully-populated which occupy large computer memory. To deal with that, the fast multipole method (FMM) is introduced to energize the line integration boundary element method (LIBEM) to performs better in efficiency. In addition, to compute domain integrals with known or unknown integrand functions which are caused by heat sources or heterogeneity, a novel BEM, the adaptive orthogonal interpolation moving least squares (AOIMLS) method enhanced LIBEM, which also inherits the advantage of boundary-only discretisation, is proposed. Unlike LIBEM, which is an accurate and stable method for computing domain integrals, but only works when the mathematical expression of integral function in domain integrals is known, the AOIMLS enhanced LIBEM can compute domain integrals with known or unknown integral functions, which ensures all the nonlinear and nonhomogeneous problems can be solved without domain discretisation. In addition, the AOIMLS can adaptively avoid singular or ill-conditioned moment matrices, thus ensuring the stability of the calculation results. (2) In the second part (Part III consisting of four chapters), the thermoelastic problems and fracture problems are the main objectives. Due to considering thermal loads, domain integrals appear in the BIEs of the thermoelastic problems, and the expression of integrand functions is known or not depending on the temperature distribution given or not, the AOIMLS enhanced LIBEM is introduced to conduct thermoelasticity analysis thereby. Besides, a series of novel unified boundary integral equations based on BEM and DDM are derived for solving fracture problems and thermoelastic fracture problems in finite and infinite domains. Two sets of unified BIEs are derived for fracture problems in finite and infinite domains based on the direct BEM and DDM respectively, which can provide accurate and stable results. Another two sets of BIEs are addressed by employing indirect BEM and DDM, which cannot ensure a stable result, thereby a modified indirect BEM is proposed which performs much more stable. Moreover, a set of novel BIEs based on the direct BEM and DDM for cracked domains under thermal stress is proposed. (3) In the third part (Part IV consisting of one chapter), a high-efficiency combined BEM and discrete element method (DEM) is proposed to compute the inner stress distribution and particle breakage of particle assemblies based on the solution mapping scheme. For the stress field computation of particles with similar geometry, a template particle is used as the representative particle, so that only the related coefficient matrices of one template particle in the local coordinate system are needed to be calculated, while the coefficient matrices of the other particles, can be obtained by mapping between the local and global coordinate systems. Thus, the combined BEM and DEM is much more effective when modelling a large-scale particle system with a small number of distinct possible particle shapes. Furthermore, with the help of the Hoek-Brown criterion, the possible cracks or breakage paths of a particle can be obtained

A new radial basis integration method applied to the boundary element analysis of 2D scalar wave equations

A new integration method named the Radial Basis Integration Method (RBIM) that include the Kriging Integration Method (KIM) Narváez and Useche (2020) as a particular case and performs boundary only offline precomputations for the creation of a meshless quadrature was developed for its application in boundary elements. Herein, as in DR-BEM, the inertial term is approximated using radial basis functions, however, its particular solution is not needed. The quadrature is now obtained in a simpler way than in KIM, because the evaluations of domain integrals necessary to compute the weights of quadrature points, is done transforming those to the boundary instead of using the Cartesian Transformation Method. Using RBIM, weakly singular domain integrals may be computed with good accuracy over complex domains. The results obtained in some scalar wave propagation problems using both Houbolt-a and Newmark-a time marching methods show that this procedure can be even more accurate than other used in BEM analysi

A Coupled BEM-MLPG Technique for the Thermal Analysis of Non-Homogeneous Media

This paper presents a technique that couples the boundary element method (BEM) with the meshless local Petrov-Galerkin (MLPG) method, formulated in the frequency domain. It is then used to study the transient heat diffusion through a two-dimensional unbounded medium containing confined subdomains where the material properties vary from point to point. To exploit the advantages of each method, the BEM is used for the homogeneous unbounded domain and the MLPG method is used for the non-homogeneous confined subdomains. The nodal points placed at the interface between the confined subdomains and the unbounded homogenous medium are used to couple the BEM and the MPLG method. The MLPG method is formulated using the moving leastsquares (MLS) approximation as the trial function and the Heaviside step function as the test function in local integral equations defined over small local sub-domains. The coupled BEM-MLPG approach is verified against the results provided by an analytical solution developed for a circular confined subdomain, in which the thermal diffusivity within the circular non-homogeneous region is assumed to vary in the radial direction. The proposed model is finally used to solve the case of a pair of non-homogeneous confined subdomains for which analytical solutions are not known. The analysis of time domain temperature responses is presented, which illustrates the applicability of the model

Meshless LocalWeak form Method Based on a Combined Basis Function for Numerical Investigation of Brusselator Model and Spike Dynamics in the Gierer-Meinhardt System

In this paper, at first, a new combined shape function is proposed. Then, based on this shape function, the meshless local weak form method is applied to find the numerical solution of time-dependent non-linear Brusselator and Gierer- Meinhardt systems. The combined shape function inherits the properties of radial point interpolation (RPI), moving least squares (MLS) and moving Kriging (MK) shape functions and is controlled by control parameters, which take different values in the domain [0;1]. The combined shape function provides synchronic use of different shape functions and this leads to more flexibility in the used method. The main aim of this paper is to show that the combined basis function can be used as a shape function in meshless local weak form methods and leads to better results in solving the system of non-linear partial differential equations especially Brusselator and Gierer-Meinhardt systems. The numerical results confirm the good efficiency of the proposed method for solving non-linear Brusselator and Gierer-Meinhardt systems

SOLID-SHELL FINITE ELEMENT MODELS FOR EXPLICIT SIMULATIONS OF CRACK PROPAGATION IN THIN STRUCTURES

Crack propagation in thin shell structures due to cutting is conveniently simulated using explicit finite element approaches, in view of the high nonlinearity of the problem. Solidshell elements are usually preferred for the discretization in the presence of complex material behavior and degradation phenomena such as delamination, since they allow for a correct representation of the thickness geometry. However, in solid-shell elements the small thickness leads to a very high maximum eigenfrequency, which imply very small stable time-steps. A new selective mass scaling technique is proposed to increase the time-step size without affecting accuracy. New ”directional” cohesive interface elements are used in conjunction with selective mass scaling to account for the interaction with a sharp blade in cutting processes of thin ductile shells

Analysis of Subsea Buried Pipelines and Partially Buried Cables

This research investigation addresses the analysis and numerical simulation of two very important offshore engineering problems. The first deals with the modeling of the steady state thermal field around buried pipelines conveying high temperature wellhead mixtures of oil and gas, and their associated dissolved impurities. These pipelines may be buried using robotic trenching equipment for physical protection or to provide additional thermal insulation. The solution to this complex multi-layer problem is examined using a boundary element model approach. The second challenging problem is that of modeling a partially buried cable on the seafloor that is ensnared by commercial fishing equipment. There are many cables on the seafloor and several obvious systems are oceanic communication cables and the increasing number of subsea power transmission systems associated with the continuing development of offshore wind farms. In this problem an important numerical modeling challenge is to allow the cable to change its length as a result of the entanglement. A different approach is presented, i.e. a meshfree formulation, is specifically developed for simulating this type of subsea cable problem. A two-dimensional boundary element model was developed specifically to investigate the local steady-state thermal field in the near field of the pipeline. Subsequently, a parametric study was preformed to evaluate the influence of the thermal power loss, burial depth, pipe diameter and soil thermal conductivity on the thermal field. The numerical examples illustrate the significant influence of the backfill thermal property on the temperature at the pipe wall, that the pipe diameter controls the required output thermal power needed to maintain the desired pipe wall temperature, and the importance of pipeline burial depth on seabed temperature distribution above the pipeline. In order to better address the problem of partially buried subsea cables, a three dimensional meshfree method was formulated and implemented to evaluate the structural response of cables in two dimensional space under accidental loads from trawling activities. The methodology specifically was developed to allow the arbitrary layout of a cable on the seafloor, the lengthening of an ensnared cable length at a boundary, and the inclusion of geometrical nonlinearity due to large deflection. This meshfree method is based upon a slender rod formulation, incorporates radial basis functions (RBF) for shape function construction, and utilizes a Galerkin weak formulation for the discretization of governing equations. The methodology was validated against two benchmark examples which have analytical solutions, and shows good convergence rates to the analytical solutions. Finally, a two dimensional gear-cable example illustrating the adaptive nature of this formulation and implementation to address a sliding length boundary condition is presented

Analisa Konduksi Panas Dua Dimensi pada Functionally Graded Materials (FGMs) Menggunakan Metode Elemen Hingga (FEM)

Seiring dengan kemajuan dunia industri, seperti industri penerbangan, kesehatan, kimia, elektronik, dan lain sebagainya, kebutuhan akan material komposit semakin meningkat untuk memenuhi permintaan pasar. Hal tersebut dikarenakan material komposit memiliki rasio beban dan berat yang tinggi dan ketahanan fatik yang baik. Namun demikian, keperluan terhadap material yang memiliki sifat-sifat ketahanan terhadap temperatur tinggi, ketahanan terhadap oksidasi juga meningkat. Functionally Graded Materials (FGMs) adalah kelas material maju dari material komposit yang memiliki sifat material yang bervariasi dari satu titik ke titik lainnya. Sifat tersebut terbentuk dari dua atau lebih fase konstituen dengan gradasi dan sifat material khusus. Pada penelitian ini akan dilakukan analisis dua dimensi konduksi panas dalam FGMs menggunakan Metode Elemen Hingga (FEM). Tiga model gradasi sifat FGMs diteliti dalam studi yaitu Polinomial, Eksponensial dan Trigonometri. Respon temperatur dari FGMs dengan menggunakan ketiga model gradasi tersebut dibandingkan dan dianalisa. Distribusi temperatur optimum tiga model yang dibangun dengan perangkat lunak ANSYS. Jika ditinjau dari variasi FGMs yang digunakan untuk permasalahan konduksi panas, variasi trigonometri dihasilkan hasil yang baik. Misalkan pada geometri silinder berlubang, nilai temperatur rata-rata yang didapat sebesar �=30,3447 . Pada geometri persegi sebesar �=46,0835 . Dan pada geometri rumit sebesar �=25,2129 . Kemudian jika ditinjau dari performa, pada geometri silinder berlubang variasi kuadratik dengan jumlah nodal 1379, didapatkan waktu pengerjaan selama 434,6 s. Pada geometri silinder berlubang variasi eksponensial, waktu pengerjaan selama 435 s. Dan pada geometri silinder berlubang variasi trigonometri, waktu pengerjaan selama 444 s. Pada geometri persegi, didapatkan waktu pengerjaan yang rata-rata sama yakni selama 37 s. Dan pada geometri rumit didapatkan waktu pengerjaan yang rata-rata sama juga yakni selama 35 s. Dan yang terakhir jika ditinjau dari efisiensi, hasil dari FEM sangat mendekati hasil dari metode analitik. Misalkan pada geometri silinder berlubang variasi kuadratik dengan jumlah nodal 761, didapatkan rata-rata nilai error sebesar 0,0019. Pada geometri silinder berlubang variasi kuadratik dengan jumlah nodal 883, rata-rata nilai error sebesar 0,0013. Dan pada geometri silinder berlubang variasi kuadratik dengan jumlah nodal 1379, rata-rata nilai error sebesar 0,0012. ============================================================================================== Along with the progress of the industrial world, such as aviation industry, healthcare, chemical, electronics, etc., the n eed for composite materials is increasing to meet market demand. This is because composite materials have a high load and weight ratio and good fatigue resistance. However, the need for materials with high temperature resistance properties, resistance to o xidation also increases. Functionally Graded Materials (FGMs) are advanced material classes of composite materials that have material properties that vary from one point to another. These properties are formed from two or more constituent phases with grada tions and special material properties. In this research will be conducted two - dimensional analysis of heat conduction in FGMs using Finite Element Method (FEM). Three models of gradation of FGMs properties were studied in the study of Polynomial, Exponenti al and Trigonometry. The temperature response of FGMs using the three gradation models is compared and analyzed. The optimum temperature distribution of three models built with ANSYS software. When viewed from the variations of FGMs used for heat conduction problems, trigonometric variations yielded good results. Suppose that in the cylinder geometry of the hole, the average temperature value obtained for T = 30,3447 oC. On a square geometry of T = 46,0835 oC. And on the complicated geometry of T = 25,2129 oC. Then, in terms of performance, the cylindrical geometry of quadratic variation with the number of nodal 1379, obtained the processing time for 434.6 s. In hollow cylindrical geometry of expone ntial variation, the processing time is 435 s. And on the cylinder geometry of the variation of trigonometry, the working time is 444 s. In rectangular geometry, the average working time is reached for 37 s. And in the complex geometry obtained the average workmanship time is also equal for 35 s. And finally, in terms of efficiency, the results of FEM are very close to the results of the analytic method. Suppose that in the cylindrical geometry of quadratic variation with the number of nodal 761, obtained a n average error value of 0.0019. In the cylindrical geometry of quadratic variation with the numeral number 883, the average error value is 0.0013. And on the cylindrical geometry of quadratic variation with the numal number 1379, the average error value is 0.0012

MAGNETOHİDRODİNAMİK KANAL AKIŞLARININ KARŞILIKLI SINIR ELEMANLARI METODU İLE ÇÖZÜMÜ

In the thesis, four different MHD duct flow problems are solved by using the Dual Reciprocity Boundary Element Method (DRBEM) with the suitable boundary conditions according to the physics of the problem. The two-dimensional, steady or unsteady, fully-developed MHD flow of a viscous, incompressible and electrically conducting fluid is considered in a long pipe of rectangular cross-section (duct) under the effect of an externally applied magnetic field which is either uniform or time-dependent or axially changing. The inductionless MHD flow with temperature dependent viscosity and heat transfer is the first considered problem. In this problem, the induced magnetic field is neglected due to the small magnetic Reynolds number assumption. Secondly, the MHD duct flow under a time-varied external magnetic field is studied. Then, we turn our concern to MHD flow problems under an axial-dependent magnetic field varying in the streamwise direction (pipe-axis direction) in the third and the fourth problems. Specifically, the inductionless MHD flow with electric potential is considered under the effect of the axially-changing magnetic field as the third problem. Adding the induced magnetic field to the velocity and electric potential equations as a triple is the last MHD flow problem considered in the thesis. The parametrix BEM implementation is also presented for the solution of the variable coefficient convection-diffusion type equations. The influence of the magnetic fields on the MHD flows is investigated and simulated in terms of the velocity, temperature, induced magnetic field and electric potential contours for several values of physical parameters.Bu tezde, dört farklı Magnetohidrodinamik (MHD) kanal akış problemi, problemin fiziğine göre uygun sınır koşulları ile birlikte karşılıklı sınır elemanları metodu (DRBEM) kullanılarak çözülmüştür. Viskoz, sıkıştırılamaz ve elektrik ileten sıvının dikdörtgen kesitli bir kanal içerisindeki iki boyutlu, zamana bağlı veya zamandan bağımsız tam gelişmiş akışı dışarıdan uygulanan bir manyetik alan etkisinde incelenmiştir. Akışı etkileyen manyetik alan ya tek düzedir ya zamana bağlıdır ya da eksenel olarak değişmektedir. Ele alınan ilk problem, sıcaklığa bağlı viskoziteye ve ısı transferine sahip indüksiyonsuz MHD akışıdır. Bu problemde, indüklenen manyetik alan küçük manyetik Reynolds sayısı varsayımından dolayı ihmal edilmiştir. İkinci problem olarak, dışarıdan uygulanan ve zamana bağlı manyetik alan etkisindeki MHD akış çalışılmıştır. Daha sonra ise, üçüncü ve dördüncü problem olarak akım yönündeki eksen boyunca değişen bir manyetik alan etkisindeki MHD akış problemleri çözülmüştür. Üçüncü problemdeki MHD akışı elektrik potansiyeline sahip fakat indüksiyonsuz bir akıştır. Dördüncü problemde ise üçüncü problemdeki MHD akışa indüklenen manyetik alan eklenerek problem denklemleri hız, elektrik potansiyel ve indüklenen manyetik alan olarak üçlü çözülmüştür. Değişken katsayılı konveksiyon-difüzyon tipi denklemlerin çözümü için parametre sınır elemanı metodu (parametrix BEM) da kullanılmıştır. Uygulanan manyetik alanların MHD akışlarına etkisi, çeşitli fiziksel problem parametre değerleri için hız, sıcaklık, indüklenen manyetik alan ve elektrik potansiyeli açısından incelenmiş ve simülasyonları yapılmıştır.Ph.D. - Doctoral Progra