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"ABSTRAKAnalisis Isogeometrik adalah pengembangan dari Metode Elemen Hingga (MEH). Analisis Isogeometrik, tidak menggunakan fungsi polinomial seperti dalam MEH, namun menggunakan fungsi Non-Uniform Rational B-Splines (NURBS) yang dipakai pada program Computer Aided Design (CAD). Diharapkan, gambar model dari CAD langsung dilakukan analisis struktur tanpa perlu dimodelkan ulang dalam program Computer Aided Engineering (CAE). Sehingga Analisis Isogeometik menjadi jembatan antara CAD dengan CAE. Dalam karya tulis ini, bahasan difokuskan dalam analisis Isogeometrik menggunakan metode Galerkin pada Balok Timoshenko dan Pelat Reissner-Mindlin dengan peralihan translasi lentur sebagai variabel tunggal. Akan dilakukan uji konvergensi untuk melihat performa dari Analisis Isogeometrik.

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ABSTRACTIsogeometric Analysis is a development of Finite Element Method (FEM). It doesn't use classical polynomial function like FEM but using Non Uniform Rational B-Splines (NURBS) function that used in Computer Aided Design (CAD) program. In the future, after drawing model with CAD, structural analysis can be done directly, not remodeling in Computer Aided Engineering (CAE) program. Conclusions, Isogeometric become bridge between CAD and CAE. In this paper, we focus for Timoshenko Beam and Reissner-Mindlin Plate with bending displacement as single variable using Galerkin Method for Isogeometric Analysis. The output of this paper is Convergence Test to learn Isogeometric "

"ABSTRAKAnalisis Isogeometrik (IGA) merupakan pengembangan dari Metode Elemen Hingga (FEM). IGA lahir untuk menjembatani Computer Aided Engineering (CAE), yang berbasiskan FEM dengan shape function polinomial, dan Computer Aided Design (CAD), yang menggunakan basis function NURBS, dengan mengaplikasikan penggunaan NURBS pada CAE agar dapat memodelkan struktur secara eksak. Skripsi ini mempelajari performa metode collocation pada IGA untuk Balok Timoshenko dan Pelat Reissner-Mindlin dengan peralihan lentur sebagai variabel tunggal melalui uji konvergensi. Pengujian mencakup peralihan dan gaya dalam, dan dibandingkan dengan metode Galerkin. Hasil pengujian menunjukkan konvergensi yang baik pada semua kasus yang diujikan.

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ABSTRACTIsogeometric Analysis (IGA) is a development of Finite Element Method (FEM). IGA was initiated to bridge Computer Aided Engineering (CAE), FEM-based program with polinomial shape function, and Computer Aided Design (CAD), which uses NURBS as basis function, by applying NURBS in CAE, so structure can be modelized exactly. This report is studying collocation method performance in IGA for Timoshenko Beam and Reissner-Mindlin Plate with bending displacement as single variable through convergence test. The test is including displacement and internal forces study, and compared to Galerkin method. The results of this study have a good convergency in every tested cases."

"Penelitian ini membahas pengaruh faktor koreksi geser (Shear Correction Factor) pada analisis statis balok Functionally Graded Material (FGM) penampang rektangular dengan metode elemen hingga (MEH) menggunakan elemen Timoshenko Hencky Beam (THB). Modulus Young yang digunakan pada balok bervariasi sepanjang ketebalan balok berdasarkan fungsi power law. Poisson ratio yang digunakan dianggap konstan. Perpindahan dengan faktor koreksi geser konstan dan perpindahan dengan faktor koreksi geser FGM akan dievaluasi untuk dua kasus dengan rasio perbandingan Modulus Young berbeda dan enam perletakan berbeda pada masing masing rasio. Komputasi numerik penelitian ini dilakukan dengan bantuan program MATLAB. Hasil penelitian menggambarkan bahwa pada balok tebal dengan material dengan rasio modulus Young kecil (0,35) faktor koreksi geser tidak terlalu berpengaruh, sedangkan pada material dengan rasio modulus Young tinggi (20) maka nilai faktor koreksi geser yang dipakai berpengaruh cukup signifikan pada nilai perpindahan yang dihasilkan.......This study is about effect of Shear Correction Factor on static analysis of a functionally graded material (FGM) beam with rectangular cross section using Finite Element Method (FEM) with Timoshenko Hencky Beam (THB) element. Young Modulus used in this study is vary continuously in the thickness direction of the beam according to Power Law form. Poisson ratio used in this study is constant. Displacement resulted by constant shear correction factor and displacement resulted by shear correction factor with FGM theory are examined with two different Modulus Young ratio and six different constraint condition on each ratio. The numerical study is done using MATLAB programs. This study shows that in thick FGM beam with small Young modulus ratio (0,35), shear correction factor did not have much effect on the displacement. Though, in FGM beam with high Young modulus ratio (20), shear correction factor used in the calculation have a significant effect on the displacement."

"Proses peleburan ferronikel di Indonesia menciptakan produk limbah berupa terak nikel yang mencapai 13 juta ton metrik per tahun. Salah satu bentuk penggunaan dan pemanfaatan limbah terak nikel adalah sebagai substitusi agregat halus dalam beton. Beton dengan agregat halus terak nikel tercatat memiliki performa yang cukup menjanjikan berdasarkan uji kekuatan berbagai penelitian. Tesis ini bertujuan untuk menganalisis perilaku mekanik balok beton bertulang dengan ukuran 15x25x300 cm3 dengan substitusi agregat halus terak nikel 50% menggunakan metode digital image correlation (DIC), serta pemodelan menggunakan elemen Multi-Fibre pada CAST3M. Spesimen beton silinder pendamping balok juga dibuat untuk mengetahui kuat tekan dan tarik dari beton. Balok diuji menggunakan uji lentur four-point loading dengan skema pembebanan semi-siklik. Hasil pengujian menunjukkan kapasitas balok terak nikel mencapai 8 tonf. Hasil pengujian juga memperlihatkan respon load-displacement balok terak nikel terlihat cukup memuaskan. Berdasarkan analisis DIC, evolusi deformasi permukaan balok akibat pembebanan dapat dipelajari untuk mengetahui pola retak yang terjadi pada permukaan balok. Selain itu, dengan pemberian beban secara semi siklik, retakan pada permukaan balok terlihat dalam analisis DIC mengalami fenomena crack opening and closing, di mana retakan kembali menutup setelah pembebanan dilepas. Namun demikian, juga tercatat bukaan retak residual dari analisis DIC. Pemodelan numerik menggunakan hukum konstitutif model kerusakan beton Mazars dan baja Elastoplastis. Terlihat respon load-displacement model dengan skema beban monotonik memberikan hasil yang cukup baik dan serupa dengan hasil eksperimen. Akan tetapi, model tersebut tidak bisa memodelkan lendutan residual balok akibat pembebanan berulang.......The Ferronickel smelting process in Indonesia creates waste products in the form of nickel slag which piled up to 13 million metric tons per year. One effort to utilize the nickel slag is to use it as a concrete fine aggregate. Concrete using nickel slag fine aggregate was reported to have promising strength results in several studies. This thesis aims to analyze the mechanical behavior of three 15x25x300 cm3 reinforced concrete (RC) beams containing nickel slag as a 50% fine aggregate substitute using the digital image correlation (DIC) method, as well as creating an RC beam model using the Timoshenko Multi-Fibre element in CAST3M. Cylindrical concrete specimens were also made to test the concrete compressive and split-tensile strength. The RC Beams were tested using a four-point loading scheme under semi-cyclic loading. Test results show the beams’ capacity had reached up to 8 tonf and their load-displacement responses show promising results. Based on DIC analysis, the evolution of deformation of the beams’ surface due to the loading can be learned to identify the crack patterns of the concrete. Furthermore, due to semi-cyclic loading, cracks on the beams’ surface were experiencing a crack opening and closing phenomenon, where the propagations of cracks ceased or reclosed throughout the unloading process. Although, residual cracks opening were also captured by DIC analysis. For modeling purposes, Mazars concrete model kerusakan and elastoplastic steel model kerusakan were used as the numerical modeling’s constitutive law. The model’s load-displacement response produced a satisfactory result compared to the experimental monotonic loading result. However, the model could not simulate residual displacements of beams due to semi-cyclic loading."

"This book provides a study aid on the finite element method. Based on the free computer algebra system Maxima, it presents routines to symbolically or numerically solve problems in the context of plane truss and frame structures. This allows readers to not only check classical hand calculations but also understand the computer implementation of the method. The mechanical theories focus on the classical one-dimensional structural elements, i.e. bars, Euler-Bernoulli and Timoshenko beams as well as their combination to generalized beam elements. Focusing on one-dimensional elements reduces the complexity of the mathematical framework and the resulting matrix equations can still be displayed with all components, and not only in a symbolic representation. The use of a computer algebra system and the incorporated functions, e.g. for equation solving, highlights the methodology of the finite element method rather than standard procedures."

"This book addresses the static and dynamic analysis of linear elastic size-dependent structures based on the modified couple stress theory. It focuses on establishing the governing equations of the size-dependent structures, deriving the associated finite element models, and implementing those models using the R programming language. The implemented functions are employed to develop a special R package (equivalent to a MATLAB toolbox) called microfiniteR for this book.In each chapter, the governing equations are formulated using the variational method, and the behaviour of the structures is examined on the basis of their load-deformation characteristics (in the case of static analyses) and by evaluating their eigenvalues (in the case of dynamics and buckling problems). The first chapter introduces readers to the R programming language, beginning with the resources needed to make use of the language and ending with a list of recommended texts. The remaining chapters cover the requisite linear elastic theory and highlight the implemented R functions. Each chapter concludes with a brief summary and relevant references. "

"This book is intended as an essential study aid for the finite element method. Based on the free computer algebra system Maxima, the authors offer routines for symbolically or numerically solving problems in the context of plane truss and frame structures, allowing readers to check classical ‘hand calculations’ on the one hand and to understand the computer implementation of the method on the other. The mechanical theories focus on the classical one-dimensional structural elements, i.e. bars, Euler–Bernoulli and Timoshenko beams, and their combination to generalized beam elements. Focusing on one-dimensional elements reduces the complexity of the mathematical framework, and the resulting matrix equations can be displayed with all components and not merely in the form of a symbolic representation. In addition, the use of a computer algebra system and the incorporated functions, e.g. for equation solving, allows readers to focus more on the methodology of the finite element method and not on standard procedures. "