We consider the numerical solution of second order Partial Differential Equations (PDEs) on lower dimensional manifolds, specifically on surfaces in three dimensional spaces. For the spatial approximation, we consider Isogeometric Analysis which facilitates the encapsulation of the exact geometrical description of the manifold in the analysis when this is represented by B–splines or NURBS. Our ...

The dynamics of beams that undergo large displacements is analyzed in frequency domain and comparisons between models derived by isogeometric analysis and p-FEM are presented. The equation of motion is derived by the principle of virtual work, assuming Timoshenko’s theory for bending and geometrical type of nonlinearity. As a result, a nonlinear system of second order ordinary differential equa...

In the context of segmenting a boundary represented solid into topological hexahedra suitable for isogeometric analysis, it is often necessary to split an existing face by constructing auxiliary curves. We consider solids represented as a collection of trimmed spline surfaces, and design a curve which can split the domain of a trimmed surface into two pieces satisfying the following criteria: t...

In this paper we construct multilevel representations in terms of a hierarchy of tensor-product generalized B-splines. These representations combine the positive properties of a non-rational model with the possibility of dealing with local refinements. We discuss their use in the context of isogeometric analysis.

We present different innovative formulations for shear deformable beams and plates exploiting the high inter-element continuity provided by NURBS basis functions. We develop isogeometric collocation methods in standard and mixed formulations as well as Galerkin methods using an alternative set of discrete variables. All methods are free of shear locking, which is confirmed by numerical tests.

This paper focuses on the numerical simulation of martensitic transformations in shape memory alloys (SMAs) using a phase-field model. We developed a dynamic thermo-mechanical model for SMAs, using strain based order parameter, having bi-directional coupling between structural and thermal physics via strain, strain rate and temperature. The model involves fourth order spatial derivatives repres...

We consider a linear full elliptic second order partial differential equation in a d-dimensional domain, d ≥ 1, approximated by isogeometric collocation methods based on uniform B-splines of degrees p := (p1, . . . , pd), pj ≥ 2, j = 1, . . . , d. We give a construction of the inherently non-symmetric matrices arising from this approximation technique and we perform an analysis of their spectra...