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"​Isogeometric finite elements combine the numerical solution of partial differential equations and the description of the computational domain given by rational splines from computer aided geometric design. This work gives a well-founded introduction to this topic and then extends isogeometric finite elements by a local refinement technique, which is essential for an efficient adaptive simulation. There by a hierarchical approach is adapted to the numerical requirements and the relevant theoretical properties of the basis are ensured. The computational results suggest the increased efficiency and the potential of this local refinement method."

"ABSTRAKMetode Elemen Hingga FEM merupakan dasar dari program CAE Computer Aided Engineering dalam menganalisis struktur dengan cara melakukan diskretisasi dengan shape function Lagrange atau Hermitian. Analisis Isogeometrik IGA merupakan perkembangan dari FEM. Dengan menggunakan Non-Uniform Rational B-Splines NURBS sebagai basis function. NURBS, yang digunakan sebagai fungsi dasar dari program CAD Computer Aided Design , permodelan dapat dilakukan secara eksak. IGA menggabungkan CAE dengan CAD sehingga permodelan CAD bisa dianalisa dengan CAE. Karya tulis ini akan memanfaatkan MATLAB dalam mempelajari penggunaan metode collocation pada analisis isogeometrik untuk balok dan pelat berdasarkan pendekatan UI. Ouput yang dihasilkan dari tulisan ini berupa peralihan translasi dan gaya dalam. Selain itu juga dilakukan uji konvergensi untuk mengecek performa metode ini.

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ABSTRACTFinite Element Method FEM is a basis of CAE program Computer Aided Engineering in structural analysis with discretization of model either with Lagrange or Hermitian shape function. Isogeometric Analysis IGA is a development of FEM. By using Non Uniform Rational B Splines NURBS as a basis function. NURBS, which is used as a basis function of CAD program Computer Aided Design , could modelized the exact model. IGA is combining concept of CAE and CAD, so the structure in CAD can be modelized in CAE. This paper is studying of utilizing MATLAB for the collocation method in isogeometric analysis for beam and plate based on UI approach. The output of this study are including displacement and internal forces. Convergence test is also presented in this paper to check this method rsquo s performance."

"ABSTRAKTeori 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."

"This self-contained book addresses the three most popular computational methods in CAE (finite elements, boundary elements, collocation methods) in a unified way, bridging the gap between CAD and CAE.It includes applications to a broad spectrum of engineering (benchmark) application problems, such as elasto-statics/dynamics and potential problems (thermal, acoustics, electrostatics). It also provides a large number of test cases, with full documentation of original sources, making it a valuable resource for any student or researcher in FEA-related areas."

"This book contains manuscripts of topics related to numerical modeling in Civil Engineering (Volume 1) as part of the proceedings of the 1st International Conference on Numerical Modeling in Engineering (NME 2018), which was held in the city of Ghent, Belgium. The overall objective of the conference is to bring together international scientists and engineers in academia and industry in fields related to advanced numerical techniques, such as FEM, BEM, IGA, etc., and their applications to a wide range of engineering disciplines. This volume covers industrial engineering applications of numerical simulations to Civil Engineering, including: Bridges and dams, Cyclic loading, Fluid dynamics, Structural mechanics, Geotechnical engineering, Thermal analysis, Reinforced concrete structures, Steel structures, Composite structures."

"This book gathers outstanding papers on numerical modeling in Mechanical Engineering (Volume 2) as part of the proceedings of the 1st International Conference on Numerical Modeling in Engineering (NME 2018), which was held in Ghent, Belgium. The overall objective of the conference was to bring together international scientists and engineers in academia and industry from fields related to advanced numerical techniques, such as the finite element method (FEM), boundary element method (BEM), isogeometric analysis (IGA), etc., and their applications to a wide range of engineering disciplines. This book addresses various industrial engineering applications of numerical simulations to Mechanical and Materials Engineering, including: Aerospace applications, Acoustic analysis, Biomechanical applications, Contact problems and wear, Heat transfer analysis, Vibration and dynamics, Transient analysis, Nonlinear analysis, Composite materials, Polymers, Metal alloys, Fracture mechanics, Fatigue of materials, Creep behavior, Phase transformation, and Crystal plasticity."