Isogeometric Finite Element Analysis Research Articles

Geometrically nonlinear NURBS isogeometric finite element analysis of laminated composite plates

This research present the development of geometrically nonlinear NURBS isogeometric finite element analysis of laminated composite plates. First-order, shear-deformable laminate composite plate theory is utilized in deriving the governing equations using a variational formulation. Geometric nonlinearity is accounted for in Von-Karman sense. A family of NURBS elements are constructed from refinement processes and validated using various examples. k-refined NURBS elements are developed to study thin plates. Isotropic, orthotropic and laminated composite plates are studied for various boundary conditions, length to thickness ratios and ply-angles. Computed center deflection is found to be in an excellent agreement with the literature. For thin plate analysis, linear and k-refined quadratic NURBS element is found to remedy the shear locking problem. k-refined quadratic NURBS element provide stabilized response to distorted, coarse meshes without increasing the order of the polynomial, owing to the increased smoothness of solution space.

A strain smoothing formulation for NURBS-based isogeometric finite element analysis

National Natural Science Foundation of China [10972188]; China Ministry of Education [NCET-09-0678]; Fundamental Research Funds for the Central Universities of China [2010121073]

Mathematical modeling of coupled drug and drug-encapsulated nanoparticle transport in patient-specific coronary artery walls

The majority of heart attacks occur when there is a sudden rupture of atherosclerotic plaque, exposing prothrombotic emboli to coronary blood flow, forming clots that can cause blockages of the arterial lumen. Diseased arteries can be treated with drugs delivered locally to vulnerable plaques. The objective of this work was to develop a computational tool-set to support the design and analysis of a catheter-based nanoparticulate drug delivery system to treat vulnerable plaques and diffuse atherosclerosis. A three-dimensional mathematical model of coupled mass transport of drug and drug-encapsulated nanoparticles was developed and solved numerically utilizing isogeometric finite element analysis. Simulations were run on a patient-specific multilayered coronary artery wall segment with a vulnerable plaque and the effect of artery and plaque inhomogeneity was analyzed. The method captured trends observed in local drug delivery and demonstrated potential for optimizing drug design parameters, including delivery location, nanoparticle surface properties, and drug release rate.

Isogeometric finite element analysis using polynomial splines over hierarchical T-meshes

Isogeometric finite element analysis has become a powerful alternative to standard finite elements due to their flexibility in handling complex geometries. One major drawback of NURBS based isogeometric finite elements is their less effectiveness of local refinement. In this study, we present an alternative to NURBS based isogeometric finite elements that allow for local refinement. The idea is based on polynomial splines and exploits the flexibility of T-meshes for local refinement. The shape functions satisfy important properties such as non-negativity, local support and partition of unity. We will demonstrate the efficiency of the proposed method by two numerical examples.