We develop a rational biquadratic G analogue of the non-uniform C B-spline paradigm. These G splines can exactly reproduce parts of multiple basic shapes, such as cyclides and quadrics, and combine them into one smoothly-connected structure. This enables a design process that starts with basic shapes, re-pepresents them in spline form and uses the spline form to provide shape handles for locali...

Beta-splines are a class of splines with applications in the construction of curves and surfaces for computer-aided geometric design. One of the salient features of the Beta-spline is that the curves and surfaces thus constructed are geometrically continuous, a more general notion of continuity than the one used in ordinary B-splines. The basic building block for Beta-splines of order k is a se...

We present an efficient algorithm for subdividing non-uniform B-splines of arbitrary degree in a manner similar to the Lane-Riesenfeld subdivision algorithm for uniform Bsplines of arbitrary degree. Our algorithm consists of doubling the control points followed by d rounds of non-uniform averaging similar to the d rounds of uniform averaging in the Lane-Riesenfeld algorithm for uniform B-spline...

this article is devoted to the simultaneous optimization of shape and topology of shell structures. the optimum shape is obtained together with the optimum layout for the reinforcement layers at the both sides of the shell surface. to solve this problem the finite element method is employed. it is assumed that each element is comprised of a porous media with microscopic rectangular voids where ...

A novel adaptive local surface refinement technique based on Locally Refined Non-Uniform Rational B-Splines (LR NURBS) is presented. LR NURBS can model complex geometries exactly and are the rational extension of LR B-splines. The local representation of the parameter space overcomes the drawback of non-existent local refinement in standard NURBS-based isogeometric analysis. For a convenient em...

In this paper, a novel and effective formulation based on isogeometric approach (IGA) and Refined Plate Theory (RPT) is proposed to study the behavior of laminated composite plates. Using many kinds of higher-order distributed functions, RPT model naturally satisfies the traction-free boundary conditions at plate surfaces and describes the non-linear distribution of shear stresses without requi...

In this paper, we present an effectively numerical approach based on isogeometric analysis (IGA) and higher-order shear deformation theory (HSDT) for geometrically nonlinear analysis of laminated composite plates. The HSDT allows us to approximate displacement field that ensures by itself the realistic shear strain energy part without shear correction factors. IGA utilizing basis functions name...

We propose in this paper a novel inverse tangent transverse shear deformation formulation for functionally graded material (FGM) plates. The isogeometric finite element analysis (IGA) of static, free vibration and buckling problems of FGM plates is then addressed using a refined plate theory (RPT). The RPT enables us to describe the non-linear distribution of shear stresses through the plate th...