Titlebook: An Isogeometric Approach to Beam Structures; Bridging the Classic Buntara S. Gan Book 2018 Springer International Publishing AG 2018 Beam e

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Numerical Integration, a line. In the finite element formulation of general beam element, we will deal with curvilinear coordinate, Jacobian operator, and curvature of a general curved beam element where the integration must be done numerically. To stick with the most basic concepts of beam element formulation using nume

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Finite Element Formulation of Beam Elements,ed on the Euler-Bernoulli and Timoshenko theories. The kinematic assumptions, governing equations via Hamilton’s principle and matrix formulations by using shape functions, are described in detail. In constructing the beam element formulations, the shape functions which are derived from the homogene

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Isogeometric Approach to Beam Element,S functions as either the geometry or the shape functions to various types of beam formulations on a plane is highlighted in detail and accompanied by MATLAB program lists. This chapter will use the program lists and concept of the NURBS from Chap. 1. The numerical integration introduced in Chap. 2

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Condensation Method, Inevitably, the computing efforts are increasing exponentially with the higher degree of real geometry to be taken into design analyses. The idea of condensing the increasing number of degrees of freedom using Isogeometric modeling is the utmost important for beam analysis practitioners. The formul

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Free Curved Beam Element Examples,e least element number which is necessary. The numerical solutions for the examples in static and free vibration problems are presented to show the effectiveness of the NURBS functions in modeling free curved beams.

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Book 2018 conventional two-node beam elements. In this volume, the author defines the Buntara Condensation Formulation: a unique formulation in condensing the dynamic equilibrium equation for beam structures, suitable for reducing the number of unlimited dynamic equations necessary to yield a classic two-nod

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Representation of Curves on a Plane,. The objective of this chapter is to bring the reader to understand the concept of the nonuniform rational B-spline (NURBS) which is the basis foundation for the construction of beam element formulations in the Isogeometric approach.

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Isogeometric Approach to Beam Element,will be adopted in constructing the beam element matrices from the NURBS functions. Based on the beam theories developed in Chap. 3, the implementation of the isogeometric approach to beam element will be discussed.

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https://doi.org/10.1007/978-3-642-51407-4. The objective of this chapter is to bring the reader to understand the concept of the nonuniform rational B-spline (NURBS) which is the basis foundation for the construction of beam element formulations in the Isogeometric approach.

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Die kulturelle Bedeutung von Bildernwill be adopted in constructing the beam element matrices from the NURBS functions. Based on the beam theories developed in Chap. 3, the implementation of the isogeometric approach to beam element will be discussed.