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Abstrak :
ABSTRAK
Teori UI-Beam adalah suatu teori baru dalam Metode Elemen Hingga (MEH) yang merupakan modifikasi dari teori Balok Timoshenko. Sementara itu Isogeometrik sendiri adalah pengembangan dari MEH yang menggunakan fungsi dari B-Splines, dimana fungsi ini menggantikan shape function dalam MEH. Kelebihan dari Isogeometrik adalah dapat menghasilkan kelengkungan geometri yang sempurna walaupun hanya menggunakan sedikit elemen. Skripsi ini berfokus pada kasus balok di atas pondasi elastis variabel tunggal, dimana hasil antara MEH dan Isogeometrik akan dibandingkan dengan eksak.

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ABSTRACT

The theory of UI-Beam happens to be the new thesis within the Finite Element Method (FEM) which is a modification of the Timoshenko Beam. Meanwhile, Isogeometric Method is a development of FEM itself that it uses B-Spline function to replace the shape function in FEM. The capability of Isogeometric Method to produce a perfect geometry curvature albeit using only a few elements becomes its adequate advantage. This paper concerns about single variable beam on the elastic foundation case which, later on, will lay a comparison between FEM, Isogeometric Method, the exact solution forward.

Abstrak :
The finite element method (FEM) has become the most widely accepted general-purpose technique for numerical simulations in engineering and applied mathematics. Principal applications arise in continuum mechanics, fluid flow, thermodynamics, and field theory. In these areas, computational methods are essential and benefit strongly from the enormous advances in computer technology. B-splines play an important role in approximation and geometric modeling. They are used in data fitting, computer-aided design (CAD), automated manufacturing (CAM), and computer graphics. Finite Element Methods with B-Splines describes new weighted approximation techniques, combining the computational advantages of B-splines and standard finite elements. In particular, no grid generation is necessary, which eliminates a difficult and often time-consuming preprocessing step. The meshless methods are very efficient and yield highly accurate solutions with relatively few parameters. This is illustrated for typical boundary value problems in fluid flow, heat conduction, and elasticity. Topics discussed by the author include basic finite element theory, algorithms for B-splines, weighted bases, stability and error estimates, multigrid techniques, applications, and numerical examples. The text is essentially self-contained and easily accessible to graduate students in mathematics, engineering, and computer sciences. The new concepts are also of interest to academic researchers and to scientists in industry who are developing finite element software. Some basic facts on functional analysis and partial differential equations, which are required, are listed in the appendix.

Abstrak :
This book is designed to supplement standard texts and teaching material in the areas of differential equations in engineering such as in Electrical ,Mechanical and Biomedical engineering. Emphasis is placed on the Boundary Value Problems that are often met in these fields.This keeps the the spectrum of the book rather focussed .The book has basically emerged from the need in the authors lectures on “Advanced Numerical Methods in Biomedical Engineering” at Yeditepe University and it is aimed to assist the students in solving general and application specific problems in Science and Engineering at upper-undergraduate and graduate level.Majority of the problems given in this book are self-contained and have varying levels of difficulty to encourage the student. Problems that deal with MATLAB simulations are particularly intended to guide the student to understand the nature and demystify theoretical aspects of these problems. Relevant references are included at the end of each chapter. Here one will also find large number of software that supplements this book in the form of MATLAB script (.m files). The name of the files used for the solution of a problem are indicated at the end of each corresponding problem statement. There are also some exercises left to students as homework assignments in the book. An outstanding feature of the book is the large number and variety of the solved problems that are included in it. Some of these problems can be found relatively simple, while others are more challenging and used for research projects. All solutions to the problems and script files included in the book have been tested using recent MATLAB software. The features and the content of this book will be most useful to the students studying in Engineering fields, at different levels of their education (upper undergraduate-graduate).