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Improved Meshless Methods and Their Engineering Applications

Thesis Info

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Author

Khan, Wajid

Program

PhD

Institute

University of Engineering and Technology

City

Peshawar

Province

KPK

Country

Pakistan

Thesis Completing Year

2019

Thesis Completion Status

Completed

Subject

Mathemaics

Language

English

Link

http://prr.hec.gov.pk/jspui/bitstream/123456789/11526/1/Wajid%20khan%20maths%202019%20uet%20peshawar.pdf

Added

2021-02-17 19:49:13

Modified

2024-03-24 20:25:49

ARI ID

1676726430087

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The research work undertaken in this dissertation is comprised of two parts. The first part is concerned about the comparative study of weak and strong meshless formulations for the numerical solution of elliptic boundary value problems. Meshless methods based on weak and strong formulation provide alternate numerical solution procedures to the well established solution techniques, such as finite element methods, finite difference methods, boundary element methods and finite volume methods. The meshless weak formulation considered in this dissertation is the well-known element free Galerkin method whereas, a strong meshless formulation chosen, is the local radial basis functions collocation method. The weak meshless formulation in the form of the element free Galerkin method is proposed while incorporating the new numerical quadrature technique based on multi-resolution Haar wavelets for approximating the displacement and strain modeled by elliptic boundary value problems in one- and two-dimensional spaces. The element free Galerkin method with numerical integration based on Gaussian quadrature has also been implemented for the numerical solution of the elliptic boundary value problems. In addition, a meshless collocation method has also been proposed in strong form using the local radial basis functions collocation method for the numerical solution of the elliptic boundary value problems. A comparative study in terms of accuracy and stability of both the weak and strong meshless formulations is carried out for the elliptic boundary value problems in one- and two-dimensional spaces. The second part of the research work undertaken in this thesis is focused on the applications of meshless methods for the solutions of solid mechanics and structural optimization problems. The element free Galerkin method with numerical integration based on Haar wavelets is also used to solve one- and two-dimensional elasto-static problems. Numerical solution obtained with these methods is in excellent agreement with analytical solution. Further, the element free Galerkin method is implemented with level set method for the two-dimensional structural optimization problems for minimum compliance design. The shape and topological sensitivities are obtained by the element free Galerkin method. The proposed topology optimization method is capable of automatically inserting holes during the optimisation process using the topological derivative approach. The structural geometry is updated through the numerical solution of modified Hamilton-Jacobi type partial differential equation by the level set method. Furthermore, the element free Galerkin method has also been combined with radial basis functions in the frame work of level set method for the solution of two-dimensional structural optimization problems. Furthermore, the finite element method has also been coupled with local radial basis functions based level set method. The original Hamilton-Jacobi equation has been transformed into a system of coupled ordinary differential equations. To highlight the associated advantages and disadvantages of the radial basis functions in the framework of level set method, a comparative study has also been carried out. The proposed methods are implemented for the optimal solutions of different types of structures with application of single and multiple loads.
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مولوی عبدالحمید ندوی

مولوی عبدالحمید ندوی
یہ سطور ابھی پریس نہیں گئی تھیں کہ مولوی عبدالحمید ندوی کے انتقال کی خبر ملی، وہ بارہ بنکی کے ایک گاؤں جیسکھ پور کے رہنے والے تھے، بڑے مخلص، حق پسند اور بہی خواہ خلق تھے، ۱۹۱۹؁ء میں ندوہ میں داخل ہوئے، تحریک خلافت شباب پر تھی، حمید صاحب بھی اس سے متاثر ہوئے، اس کی وجہ سے سادگی طبیعت ثانیہ بن گئی، مولانا عبدالرحمن نگرامی کی صحبت نے ان کے اندر ندوہ کی محبت اور خاموش خدمت کا جذبہ پیدا کیا، تعلیم سے فراغت کے بعد قیام زیادہ تر وطن ہی میں رہا، لیکن ندوہ برابر آتے جاتے رہتے تھے، دوستوں کے اصرار کئی برس تک بھٹکل میں تعلیمی خدمت انجام دی، ان کے مخلص شاگردوں نے اس کام کو آگے بڑھایا اور ایک بڑا تعلیمی مرکز قائم ہوگیا، عرصہ سے دل کے مریض تھے، رمضان میں ندوہ آئے، مولانا ابوالحسن علی سے ملنے رائے بریلی جانے کا ارادہ تھا، دفعتہ دل کا دورہ پڑا اور تھوڑی دیر میں جان جان آفریں کے سپرد کردی، اﷲ تعالیٰ ان کی مغفرت فرمائے اور ان کے صاحبزادہ مولوی عبدالرشید ندوی اور دوسرے متعلقین کو صبر جمیل عطا فرمائے۔ (عبد السلام قدوائی، ستمبر ۱۹۷۸ء)

 

شیخ الحدیث مولانا سلیم اللہ خان کی تصنیفی خدمات

Sheikh Molana saleem ullah khan was born in Muzaffer Nagar in India. He belongs to hasan pur. He get degree of dura-e-nizami from Dar-ul-Uloom Deoband. In Deoband he received Education of Quran, Hadith and other related sciences through learned scholars of the time which includes Molana Hussain Ahmed Madani, Molana Izaz Ali, Molana Idrees kandahalvi and other religious personalities. After his education he start teaching and served as a teacher in many madaris. He was a prominent and renowned scholar.1n 1967 He laid the foundation of Jamia Farooqia Karachi. His entire services have been so much blessed by Almighty Allah that since its foundation, till now the Jamia has advanced a long way in Islamic Education and related fields which seems almost unbelievable. He left many books which based on his writing and narration of Hadith during different session of dura-e-Hadith. In this Article, I have tried my level best to elaborate sheikh saleem Ullah khan’s services as Author for Islamic literature and specially for Hadith Nabvi(s.w).

Synthesis of Novel Heterocyclic Compounds

The present dissertation entitled “Synthesis of Novel Heterocyclic Compounds” is comprised of two parts. Part A describes the synthesis of Azaborines. In Part A the synthesis of Azaborines is classified into two classes. (a) 1, 3, 2 benzodiazaborininones (carbonyl containing, boron-based heterocyclic scaffolds) (68-89). In the synthesis of 1, 3, 2 benzodiazaborininones, anthranilamide reacted with different commonly available potassium organitriflouroborates using a fluorophile (BF3NH2Et) with efficient methodology. NH B NH O 68 F NH B NH O MeO OMe 69 NH B NH O O 70 NH B NH O 71 NH B NH O Br 72 NH B NH O F F 73 NH B NH O COOMe 74 NH B NH O CN 75 NH B NH O 76 NH B NH O O 77 NH B N H O CH3 78 Abstract ix NH B N H O CF3 79 NH B N H O S 80 NH B NH O NO2 81 NH B NH O 82 NH B NH O 83 84 NH B NH NH2 O NH B NH Cl O 85 NH B NH O CO2Me 86 CH2CO2Me NH B NH O 87 NH B NH O 88 N H B NH N O 89 The second class of azaborines prepared were 1,2-dihydroazaborinines, including 1-benzenyl-2-quinolinyl/isoquinolinyl-1,2-dihydroazaborinines (91-95, b1). These were obtained by reacting N-benzyl-2-vinylaniline with potassium organotrifouroborates in the presence of SiCl4 and Et3N. 2-Ethynyl-1,2-dihydroazaborinines (96-97, b2) were synthesized by using the same methodology where 2-vinylaniline was used with different commercially available potassium organotriflouroborates. All the products synthesized were charecterzied by FT-IR, 1H-NMR, 13C-NMR, 11B-NMR, HRMS. The results obtained confirmed the formation of desired product. Abstract x B N N B N N B N N B N N B N N 91 92 93 94 95 B HN TMS B HN F 96 97 Part B. Part B consists of the synthesis of 2,4 di-substituted quinolines. The 2, 4- disubstituted quinolines were synthesized using a Povarov related reaction using indium chloride as a catalyst. Two classes of 2,4 di-substituted quinolines were prepared. (c) Quinoline isoindolindiones (187-193) products were synthesized in two steps.The First step involved Schiff base synthesis while second step involved condensation of Schiff bases with N-propargylphthalimide. N Cl OMe N O O N Br OMe N O O N OMe N O O MeO 187 188 189 Abstract xi N OMe N O O N OMe N O O N Cl N O O MeO N N O O 190 191 192 193 Second class is (d) benzoquinoline isoindolindiones (194,195). These compounds were prepared by reacting aldehydes, 1-naphthyl amine with N-propargylphthalimide in presence of indium chloride catalyst. All these compounds were characterized through FT-IR, 1H-NMR and 13C-NMR. Along with N-propargylphthalimide, another alkyne, 1- nitro-4-(prop-2-ynyloxy)benzene was used under the same conditions. A reaction was attempted where 1-nitro-4-(prop-2-ynyloxy)benzene was reacted with benzo[c][1,2,5]thiadiazol-5-amine and different aldehydes, but the product isolated was not the desired one. N N O O N N O O 194 195