Free vibration analysis of thin plates by using a NURBS-based isogeometric approach

Shojaee, Saeed; Izadpanah, E.; Valizadeh, Navid; Kiendl, Josef

doi:10.1016/j.finel.2012.06.005

Cited by 129 publications

(47 citation statements)

References 31 publications

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“…Although numerous plate theories have been developed since the late 19th century, the classical plate theory (CPT) [1] and the first-order shear deformation theory (FSDT) [2] are the most widely accepted and applied theories in engineering. The CPT is the simplest theory with high computational efficiency that neglects transverse shear strains and midplane displacements.…”

Section: Introductionmentioning

confidence: 99%

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Free Vibration Analyses of FGM Thin Plates by Isogeometric Analysis Based on Classical Plate Theory and Physical Neutral Surface

Yin

Liu

2013

Advances in Mechanical Engineering

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The isogeometric analysis with nonuniform rational B-spline (NURBS) based on the classical plate theory (CPT) is developed for free vibration analyses of functionally graded material (FGM) thin plates. The objective of this work is to provide an efficient and accurate numerical simulation approach for the nonhomogeneous thin plates and shells. Higher order basis functions can be easily obtained in IGA, thus the formulation of CPT based on the IGA can be simplified. For the FGM thin plates, material property gradient in the thickness direction is unsymmetrical about the midplane, so effects of midplane displacements cannot be ignored, whereas the CPT neglects midplane displacements. To eliminate the effects of midplane displacements without introducing new unknown variables, the physical neutral surface is introduced into the CPT. The approximation of the deflection field and the geometric description are performed by using the NURBS basis functions. Compared with the first-order shear deformation theory, the present method has lower memory consumption and higher efficiency. Several numerical results show that the present method yields highly accurate solutions.

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Section: Introductionmentioning

confidence: 99%

“…In the IGA, higher order NURBS basis functions can be easily obtained, so the formulation of CPT can be simplified [1,3]. The main objective of this research work is to extend CPT-based IGA to study free vibration of FGM thin plates.…”

Section: Introductionmentioning

confidence: 99%

Free Vibration Analyses of FGM Thin Plates by Isogeometric Analysis Based on Classical Plate Theory and Physical Neutral Surface

Yin

Liu

2013

Advances in Mechanical Engineering

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“…NURBS has also shown significant improvement in the analysis of structural vibration problems in terms of robustness and accuracy, by using k-refinement as compared to higher order p-refinement [13]. Similar results are evident in the analysis of structural vibration of thin plates [14].…”

Section: Introductionmentioning

confidence: 54%

Static Structural and Modal Analysis Using Isogeometric Analysis

Gondegaon¹,

Voruganti²

2016

Journal of Theoretical and Applied Mechanics

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Isogeometric Analysis (IGA) is a new analysis method for unification of Computer Aided Design (CAD) and Computer Aided Engineering (CAE). With the use of NURBS basis functions for both modelling and analysis, the bottleneck of meshing is avoided and a seamless integration is achieved. The CAD and computational geometry concepts in IGA are new to the analysis community. Though, there is a steady growth of literature, details of calculations, explanations and examples are not reported. The content of the paper is complimentary to the existing literature and addresses the gaps. It includes summary of the literature, overview of the methodology, step-by-step calculations and Matlab codes for example problems in static structural and modal analysis in 1-D and 2-D. At appropriate places, comparison with the Finite Element Analysis (FEM) is also included, so that those familiar with FEM can appreciate IGA better.KEY WORDS: Isogeometric analysis, B-spline, finite element analysis, computer aided design, Matlab.

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“…The basic IGA paradigm consists of adopting the same basis functions used for geometry representations in CAD systems -such as, e.g., Non-Uniform Rational B-Splines (NURBS) -for the approximation of field variables, in an isoparametric fashion. Thanks to the high-continuity properties of its basis functions, IGA is also characterized by an increased accuracy and robustness on a per-degree-of-freedom basis in comparison to standard FEA [3][4][5][6][7], and opens the door to new possibilities such as the construction of geometrically flexible discretizations of higher-order partial differential equations (PDEs) in primal form [8][9][10][11][12].…”

Section: Introductionmentioning

confidence: 99%