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Isogeometric analysis is a new approach in computational mechanics where the geometry and computational modeling is carried out by using NURBS and B-spline functions. The main advantage of the isogeometric approach is in unifying the discretization and problem-solving processes that lead to saving of computational time and cost. In this research, the governing equations of buckling analysis of thin plates stiffened with stiffeners with various geometries are obtained by use of the variational accounting method and first-order shear deformation theory (FSDT). The geometry of stiffener and its position on arbitrarily plate are considered. The equation of buckling is derived by employing the total potential energy, and the obtained system of equations is solved by discretization with the isogeometric analysis method. One of the main advantages of this approach is that it does not need a fine mesh for unification of the connection between the plate and its stiffeners so that, it leads to more accurate answers in comparison with other numerical methods and commercial software with the same number of unknowns. Finally, In order to verification, a few examples are presented and the obtained results are compared with the available results of the analytical and numerical method. [ABSTRACT FROM AUTHOR]

Abstract Isogeomteric Analysis is a newly developed method with some features that can be considered as ‎a potential substitute to other numerical methods such as finite elements and meshless approaches. ‎The NURBS technique, that allows precise geometrical modeling, plays an important role in this ‎method. However, similar to other numerical methods, existence of errors in the approximation of ‎the unknown function is inevitable. This paper is devoted to finding points with higher accuracy in ‎stress recovery by the isogeometric analysis. It can be shown that these points are coincident with ‎the Gauss quadrature points. By making use of these superconvergent points together with the ‎NURBS technique and the least square method, a surface is constructed for each component of ‎the stress tensor that represents the improved stresses. For this purpose, three examples with ‎available analytical results has been solved. The comparison of the obtained improved stresses ‎with the exact solution is used for the sake of verification of the proposed method. It is concluded ‎that the superconvergent points location in the isogeometric analysis are the same as the minimum ‎required Gauss points for the integration of a square element.‎

This paper presents an isogeometric analysis approach for static and free vibration analysis of laminated composite plates covered with piezoelectric layers using the Reissner-Mindlin theory. Isogeometric analysis (IGA) aims at simplifying the Computer Aided Design (CAD) and Computer Aided Engineering (CAE) by using the functions describe the geometry (CAD) and the unknown fields (Analysis). The isogeometric approach has here been employed that utilizes the Non-Uniform Rational B-Splines (NURBS) of quadratic, cubic and quartic orders to approximate the variables defining geometry as well as the unknown functions. Using the Reissner-Mindlin first order shear deformation theory requires the C0-continuity of generalized displacements and the NURBS basis functions are well suited for this purpose. The electric potential is assumed to vary linearly through the thickness for each piezoelectric sublayer. To alleviate the shear locking problem, a stabilization technique is employed in the stiffness formulation. Since study of the performance and accuracy of IGA in solving laminated composite plates is one of the main objectives of this article. Several numerical examples are presented and compared with those available in the literature. The obtained results indicate desirable accuracy and efficiency of the proposed approach. [ABSTRACT FROM AUTHOR]

This article is devoted to the derivation of formulation and isogeometric solution of nonlinear nearly incompressible elastic problems, known as nearly incompressible hyperelasticity. After problem definition, the governing equations are linearized for employing the Newton-Raphson iteration method. Then, the problem is discretized by using concepts of isogeometric analysis method and its solution algorithm is devised. To demonstrate the performance of the proposed approach, the obtained results are compared with the finite elements solutions. Due to large deformations in this kind of problems, the finite element method requires a relatively large number of elements, as well as the need for remeshing in some problems, that result in a large system of equations with a high computational cost. In the isogeometric analysis method, B-Spline and NURBS (Non-Uniform Rational B-Spline) basis functions provide a good flexibility in modeling of geometry without any need for further remeshing. The examples studied in this article indicate that by using the isogeometric approach good quality results are obtained with a smaller system of equations and less computational cost. Also, influence of different volumetric functions for the nearly incompressible materials is investigated. [ABSTRACT FROM AUTHOR]