On the equivalence between the cell-based smoothed finite element method and the virtual element method

We revisit the cell-based smoothed finite element method (SFEM) for quadrilateral elements and extend it to arbitrary polygons and polyhedrons in 2D and 3D, respectively. We highlight the similarity between the SFEM and the virtual element method (VEM). Based on the VEM, we propose a new stabilization approach to the SFEM when applied to arbitrary polygons and polyhedrons. The accuracy and the convergence properties of the SFEM are studied with a few benchmark problems in 2D and 3D linear elasticity. Later, the SFEM is combined with the scaled boundary finite element method to problems involving singularity within the framework of the linear elastic fracture mechanics in 2D

A freeform shape optimization of complex structures represented by arbitrary polygonal or polyhedral meshes

In this paper we propose a new scheme for freeform shape optimization on arbitrary polygonal or polyhedral meshes. The approach consists of three main steps: (1) surface partitioning of polygonal meshes into different patches; (2) a new freeform perturbation scheme of using the Cox–de Boor basis function over arbitrary polygonal meshes, which supports multi-resolution shape optimization and does not require CAD information; (3) freeform shape optimization of arbitrary polygonal or polyhedral meshes. Numerical experiments indicate the effectiveness of the proposed approach. Copyright © 2004 John Wiley & Sons, Ltd.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/34540/1/1050_ftp.pd

A novel haptic model and environment for maxillofacial surgical operation planning and manipulation

This paper presents a practical method and a new haptic model to support manipulations of bones and their segments during the planning of a surgical operation in a virtual environment using a haptic interface. To perform an effective dental surgery it is important to have all the operation related information of the patient available beforehand in order to plan the operation and avoid any complications. A haptic interface with a virtual and accurate patient model to support the planning of bone cuts is therefore critical, useful and necessary for the surgeons. The system proposed uses DICOM images taken from a digital tomography scanner and creates a mesh model of the filtered skull, from which the jaw bone can be isolated for further use. A novel solution for cutting the bones has been developed and it uses the haptic tool to determine and define the bone-cutting plane in the bone, and this new approach creates three new meshes of the original model. Using this approach the computational power is optimized and a real time feedback can be achieved during all bone manipulations. During the movement of the mesh cutting, a novel friction profile is predefined in the haptical system to simulate the force feedback feel of different densities in the bone

Automated generation of flat tileable patterns and 3D reduced model simulation

The computational fabrication community is developing an increasing interest in the use of patterned surfaces, which can be designed to show ornamental and unconventional aesthetics or to perform as a proper structural material with a wide range of features. Geometrically designing and controlling the deformation capabilities of these patterns in response to external stimuli is a complex task due to the large number of variables involved. This paper introduces a method for generating sets of tileable and exchangeable flat patterns as well as a model-reduction strategy that enables their mechanical simulation at interactive rates. This method is included in a design pipeline that aims to turn any general flat surface into a pattern tessellation, which is able to deform under a given loading scenario. To validate our approach, we apply it to different contexts, including real-scale 3D printed specimens, for which we compare our results with the ones provided by a ground-truth solver

A one point integration rule over star convex polytopes

In this paper, the recently proposed linearly consistent one point integration rule for the meshfree methods is extended to arbitrary polytopes. The salient feature of the proposed technique is that it requires only one integration point within each n-sided polytope as opposed to 3n in Francis et al. (2017) and 13n integration points in the conventional approach for numerically integrating the weak form in two dimensions. The essence of the proposed technique is to approximate the compatible strain by a linear smoothing function and evaluate the smoothed nodal derivatives by the discrete form of the divergence theorem at the geometric center. This is done by Taylor's expansion of the weak form which facilitates the use of the smoothed nodal derivatives acting as the stabilization term. This translates to 50% and 30% reduction in the overall computational time in the two and three dimensions, respectively, whilst preserving the accuracy and the convergence rates. Th

A new scheme for efficient and direct shape optimization of complex structures represented by polygonal meshes

In this paper, a new shape optimization approach is proposed to provide an efficient optimization solution of complex structures represented by polygonal meshes. Our approach consists of three main steps: (1) surface partitioning of polygonal meshes; (2) generation of shape design variables on the basis of partitioned surface patches; and (3) gradient-based shape optimization of the structures by reducing a weighted compliance among all load cases. The main contributions of this paper include (i) that our approach can be directly applied on polygonal meshes with the reduction of design variables or decision variables by 10 to 1000 times, compared to the conventional design variable scheme of using each mesh node; (ii) our perturbation scheme is mathematically proven with respect to maintaining the smoothness of each surface patch, except on its boundary; and (iii) overall, our approach can be used to automate time-consuming shape optimization of polygonal meshes to a greater extent. Numerical experiments have been conducted and the results indicate the effectiveness of the approach. Copyright © 2003 John Wiley & Sons, Ltd.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/34539/1/859_ftp.pd