Panayiotis S. Shiakolas

Simple algorithm for adaptive refinement of three-dimensional finite element tetrahedral meshes

A simple strategy to adaptively refine three-dimensional tetrahedral meshes has been implemented. The procedure adaptively refines a crude initial mesh using solution error indicators or other suitable measures. In this paper example problems were remeshed using a refinement ratio determined from an a posteriori error indicator obtained from the finite element solution or the problem. The resulting finite element meshes are round to have a smooth gradient in element size. Aspect ratios are calculated to determine the quality or each element, and a smoothing procedure is employed to improve the element aspect ratio. Example meshes are included to show the adaptive nature or the remesher when applied over several solution cycles

Closed-form expressions for the linear and quadratic strain tetrahedral finite elements

Abstract The use of closed-form expressions in a finite element code significantly reduces the time required to evaluate the element stiffness matrix as compared to Gaussian quadrature. The development of closed-form expressions for the element stiffness matrices for the plane-faced linear strain and quadratic strain tetrahedral finite elements has been previously presented elsewhere. In this paper, a reformulation of the process is given which significantly reduces the size of the element stiffness expressions. Expression growth is prevented by decomposing the strain-displacement matrix and utilizing a new matrix which is geometry and material dependent.

Closed-Form Expressions for Higher Order Electroelastic Tetrahedral Elements

A finite element formulation for three-dimensional modeling of dynamic and static responses of structures with piezoelectric components and the development of highly efficient closed-form expressions for element electroelastic stiffness matrices for straight-sided linear strain tetrahedral and quadratic strain tetrahedral elements are presented. Included is a discussion of procedures for combining tetrahedra to produce hexahedral elements. Two simple numerical examples are presented to illustrate the formulation.

Study on two-stage hot embossing microreplication: silicon to polymer to polymer

Hot embossing microfabrication has been used for the replication of a mold onto a polymer substrate for the past decade, with the molds usually made using techniques like wet etching, CNC machining, and laser writing. Fabricating a male mold using a laser and CNC machining consumes a lot of resources in mold design, mold fabrication time, and smooth surface finish of the mold. In this work, a novel approach called two-stage embossing that is a slight modification of the existing process is proposed. This process still requires a primary mold (of the same shape as the final desired part) that is used to emboss on a polymer of higher glass transition temperature than the substrate to be used for the second stage embossing. Finally this polymer secondary mold is used for the final replication on the desired substrate. Preliminary experimental results focusing on mold quality with respect to the number of embossing cycles of the secondary mold, the embossing quality of the final substrate as compared to the primary silicon mold, and the life of the secondary mold are presented. The experimental results confirm the viability of the process as a candidate process for hot embossing microreplication applications.

Identification and design of source term in a two-region heat conduction problem

This work deals with the use of the conjugate gradient method with adjoint problem for the estimation of an unknown source term in a two-region problem. The physical problem consists of heat conduction in two contacting rectangular regions, where the source term is known to exist in only one of them. The source term is supposed to vary in time as well as within the region. Results are presented for the inverse identification problem by using simulated temperature measurements containing random errors. In addition, results are presented for an inverse design problem with application in hot embossing microreplication microfabrication technology employed for the fabrication of polymer-based Micro-electromechanical Systems (MEMS).

Development and initial testing of a prototype concentric tube robot for surgical interventions

The development and initial testing of a prototype concentric tube robot suitable for surgical applications is presented. The system is endowed with 3 degrees-of-freedom and consists of a three concentric tubes assembly and an actuation module. Design issues are discussed in a general context of concentric tube robots in view of their potential applications in surgery. Among the distinct features of the system is that the actuation module provides a mechanical decoupling between the available motions that effectively facilitates control of the device. Such robotic systems are considered particularly suitable for MR- guided interventions and compatibility issues with the specific imaging modality are discussed. Initial experimental testing of the device is presented which involved tip targeting and steering trials using direct visual feedback for guidance.