Standard Isogeometric Analysis Research Articles

A numerical approach for dynamic analysis of solids in boundary representation

AbstractThis contribution is concerned with a numerical approach for dynamic analysis of solids in boundary representation. The aim of this investigation is to provide accurate results for the dynamic analysis in cases where only the boundary of a solid is available, whether this is defined for an open or closed domain. In CAD solids are defined through their bounded surfaces. Hence, the present method is perfectly suited to analyse such kind of geometries. The proposed approach is, therefore, based on the principle to represent a computational domain by scaling its boundary with respect to a scaling center. NURBS basis functions are used to depict the geometry of a domain and to approximate the unknowns of the problem. The core of this study is formally supported, firstly by high continuity generated by the selected interpolation functions, that provide a superior approximation for the dynamic properties of a domain, and secondly, by the adopted parametrization in boundary representation. In the entire domain, which is an elastic, homogeneous and isotropic medium under plain‐strain motion, the weak form is enforced to solve the equation of motion of the problem. An implicit method is employed for time integration. The robustness and stability of this approach are studied considering higher order NURBS basis functions to calculate superior eigenvalues of an open domain. The proposed approach is compared with the standard isogeometric analysis, which differs from the parametrization in this study, in order to show the performance of this formulation.

The effect of uncertain elastic modulus on eigenvalue in the free vibration of a functionally graded plate

Abstract This research deal with investigation of eigenvalue in stochastic free vibration problem of functionally graded (FG) plates involving uncertain elastic modulus. The governing equations of FG plate are derived using classical plate theory. The stochastic isogeometric analysis is established using the standard isogeometric analysis in conjugation with perturbation technique. An uncertain elastic modulus is hypothesized to be Gaussian random field. The result predicted by present method is validated with Monte Carlo simulation show good agreement. The effect of uncertain elastic modulus on variability in the eigenvalue of free vibration of plate is significant.

Uncertainty qualification for the free vibration of a functionally graded material plate with uncertain mass density

This work studies the response variability in the eigenvalue of free vibration of functionally graded material (FGM) plates with uncertain mass density. The mass density of plates is assumed to be a Gaussian random field on the plane of the plate. The formulation of free vibration of FGM plates is derived using isogeometric analysis based on higher-order shear deformation theory. The stochastic isogeometric analysis is established based on standard isogeometric analysis and a perturbation approach. Also, the formulation for variation of the eigenvalue of free vibration of the plate is issued. The present approach is validated with Monte Carlo simulation (MCS) based on a spectral representation method. The numerical examples investigated show good agreement between the present approach and Monte Carlo simulation. Based on the numerical results, the effect of a parameter of uncertain mass density on variability in the natural frequencies is drawn with respect to FGM plates.

Spectral approximation properties of isogeometric analysis with variable continuity

We study the spectral approximation properties of isogeometric analysis with local continuity reduction of the basis. Such continuity reduction results in a decrement in the interconnection between the degrees of freedom of the mesh, which allows for large computational savings during the solution of the resulting linear system. The continuity reduction results in extra degrees of freedom that modify the approximation properties of the method. The convergence rate of such refined isogeometric analysis is equivalent to that of the maximum continuity basis. We show how the breaks in continuity and inhomogeneity of the basis lead to artifacts in the frequency spectra, such as stopping bands and outliers, and present a unified description of these effects in finite element method, isogeometric analysis, and refined isogeometric analysis. Accuracy of the refined isogeometric analysis approximations can be improved by using non-standard quadrature rules. In particular, optimal quadrature rules lead to large reductions in the eigenvalue errors and yield two extra orders of convergence, as it occurs in standard isogeometric analysis.