Fred van Keulen

A finite-element analysis model of orbital biomechanics

To reach a better understanding of the suspension of the eye in the orbit, an orbital mechanics model based upon finite-element analysis (FEA) has been developed. The FEA model developed contains few prior assumptions or constraints (e.g., the position of the eye in the orbit), allowing modeling of complex three-dimensional tissue interactions; unlike most current models of eye motility. Active eye movements and forced ductions were simulated and showed that the supporting action of the orbital fat plays an important role in the suspension of the eye in the orbit and in stabilization of rectus muscle paths.

Effects of size and defects on the elasticity of silicon nanocantilevers

The size-dependent elastic behavior of silicon nanocantilevers and nanowires, specifically the effective Youngs modulus, has been determined by experimental measurements and theoretical investigations. The size dependence becomes more significant as the devices scale down from micro- to nano-dimensions, which has mainly been attributed to surface effects. However, discrepancies between experimental measurements and computational investigations show that there could be other influences besides surface effects. In this paper, we try to determine to what extent the surface effects, such as surface stress, surface elasticity, surface contamination and native oxide layers, influence the effective Youngs modulus of silicon nanocantilevers. For this purpose, silicon cantilevers were fabricated in the top device layer of silicon on insulator (SOI) wafers, which were thinned down to 14 nm. The effective Youngs modulus was extracted with the electrostatic pull-in instability method, recently developed by the authors (H Sadeghian et al 2009 Appl. Phys. Lett. 94 221903). In this work, the drop in the effective Youngs modulus was measured to be significant at around 150 nm thick cantilevers. The comparison between theoretical models and experimental measurements demonstrates that, although the surface effects influence the effective Youngs modulus of silicon to some extent, they alone are insufficient to explain why the effective Youngs modulus decreases prematurely. It was observed that the fabrication-induced defects abruptly increased when the device layer was thinned to below 100 nm. These defects became visible as pinholes during HF-etching. It is speculated that they could be the origin of the reduced effective Youngs modulus experimentally observed in ultra-thin silicon cantilevers.

On the size-dependent elasticity of silicon nanocantilevers: impact of defects

Recent measurements have indicated that the elastic behaviour of silicon nanocantilevers and nanowires is size-dependent. Several theoretical models have been proposed to explain this phenomenon, mainly focused on surface stress effects. However, discrepancies are found between experiments and theories, indicating that there could be other influences in addition to surface effects. One of the important issues, which was experimentally confirmed and has not been considered, is accounting for the fact that experimentally tested nanocantilevers and nanowires are not defect free. In this paper molecular dynamics (MD) is utilized to study the effects of defects on the elasticity of silicon. The effective Young’s modulus ˜ E of [100] and [110] oriented silicon nanoplates is extracted in the presence of defects, showing that such defects significantly influence the size-dependent behaviour in ˜ E. The MD results are compared with the results of continuum theory, showing that continuum theory holds, even for very small defects. Taking into account the surface effects, native oxide layers together with fabrication-induced defects, the experimental measurements can be explained. The studied example involved nanocantilevers, but can be extended to nanowires. (Some figures in this article are in colour only in the electronic version)

Efficient Finite Difference Design Sensitivities

The problem considered in this study is to evaluate efficiently displacement derivatives using global finite differences. Given the displacements for an initial design, the displacements for various modified designs are evaluated by the recently developed combined approximations method. Calculations of finite difference sensitivity coefficients are demonstrated for static problems and eigenproblems. The presented solution procedure is easy to implement, efficient, and can be used to calculate derivatives for various designs where the exact displacements are not known. Some numerical examples show that the accuracy of the results is similar to the accuracy obtained by finite difference calculations based on exact analysis.

NEW DEVELOPMENTS IN STRUCTURAL OPTIMIZATION USING ADAPTIVE MESH REFINEMENT AND MULTIPOINT APPROXIMATIONS

Combining Shape Optimization (SO) with Adaptive Mesh Refinement (AMR) potentially offers a higher accuracy and higher computational efficiency, especially if the applied target error for AMR is reduced in the course of the optimization process. The disadvantage of that approach is that the rate of convergence of the corresponding optimization processes can be significantly lower as compared to processes which apply a fixed target error for AMR. In the present paper the so-called Multipoint Approximation Method (MAM) is used as a basis for SO in conjunction with AMR. Several techniques for improvement of the rates of convergence are presented and investigated. Firstly, alternative algorithms for determining the approximation functions using a weighted least squares method are investigated. The focus is on weights which depend on the discretization errors. Secondly, different strategies for moving and resizing the search sub-regions in the space of design variables are presented. The proposed methods are il...

Nonlinear thin shell analysis using a curved triangular element

Abstract This paper describes a simple but robust curved triangular thin shell element. The element has twelve degrees of freedom, namely the displacement components in the corner nodes and the rotations about the element sides. The element is based upon the well-known facet element with constant membrane strains and constant stress couples, and is augmented to take into account the influence of the changes of curvature on the membrane deformations. Due to the quadratic character of this influence, curved geometries can be modelled. In order to permit arbitrarily large rotational increments, reference vectors are attached to each element side. These reference vectors are updated by means of orthogonal transformations. The latter are determined uniquely by the subsequent orientations of the associated element sides. The changes of curvature are evaluated using these reference vectors and a corotated reference configuration. To describe time-independent elastoplasticity, a layered shell model is applied, while Besselings fraction model is adopted for each layer. A number of numerical examples illustrate the performance of the element.

Interface micromotions increase with less-conforming cementless glenoid components

BACKGROUND The optimal degree of conformity between the glenoid and humeral components in total shoulder arthroplasty for best performance and durability is still a matter of debate. The main aim of this study is to evaluate the influence of joint conformity on the bone-implant interface micromotions in a cementless glenoid implant. MATERIALS AND METHODS Polyethylene inlays with different degrees of conformity (radial mismatch of 0, 2, 4, and 6 mm) were mounted on a cementless metal back and then implanted in a bone substitute. These glenoid components were loaded by a prosthetic humeral head during a force-controlled experiment. Normal-to-interface micromotions and bone substitute deformations were measured at different points of the interface. Rim displacement and humeral head translation were also measured. A finite element (FE) model of the experiments was implemented to estimate the normal- and tangent-to-interface micromotions in the entire bone-implant interface. RESULTS All measured variables increased with less-conforming PE inlays. Normal-to-interface micromotions were significantly larger (P < .05) when the radial mismatch was 6 mm compared with the fully conforming inlay. The FE model was in agreement and complemented the experimental results. FE model-predicted interface micromotions were already significantly larger when the radial mismatch was equal to 4 mm. DISCUSSION In a force-controlled experiment with a cementless glenoid component, a non-conforming PE inlay allows larger interface micromotions than a conforming inlay, reaching a magnitude that may hamper local bone ingrowth in this type of component. This is mainly because of the larger humeral head translation that boosts the effects of the so-called rocking-horse phenomenon.

Prediction of torsional failure in 22 cadaver femora with and without simulated subtrochanteric metastatic defects: a CT scan-based finite element analysis.

Background In metastatic bone disease, prophylactic fixation of impending long bone fracture is preferred over surgical treatment of a manifest fracture. There are no reliable guidelines for prediction of pathological fracture risk, however. We aimed to determine whether finite element (FE) models constructed from quantitative CT scans could be used for predicting pathological fracture load and location in a cadaver model of metastatic bone disease. Material and methods Subject-specific FE models were constructed from quantitative CT scans of 11 pairs of human femora. To simulate a metastatic defect, a transcortical hole was made in the subtrochanteric region in one femur of each pair. All femora were experimentally loaded in torsion until fracture. FE simulations of the experimental set-up were performed and torsional stiffness and strain energy density (SED) distribution were determined. Results In 15 of the 22 cases, locations of maximal SED fitted with the actual fracture locations. The calculated torsional stiffness of the entire femur combined with a criterion based on the local SED distribution in the FE model predicted 82% of the variance of the experimental torsional failure load. Interpretation In the future, CT scan-based FE analysis may provide a useful tool for identification of impending pathological fractures requiring prophylactic stabilization.

A geometrically nonlinear curved shell element with constant stress resultants

Abstract A curved triangular shell element with constant stress resultants and 12 degrees of freedom is presented. The degrees of freedom are the displacement components in the vertices and the rotations about the element sides. The starting point is the combination of a constant strain triangle and a flat constant bending triangle. The membrane deformations of this original flat element are modified, so that curvature changes give an essential contribution in the geometrically nonlinear regime. Initial curvature is brought into account by observing initial deflections of the flat element with modified membrane deformations. Arbitrary rotations are incorporated by means of co-rotation theory, applied to the bending behaviour only. Unconventional equivalent nodal forces for pressure loading are discussed, which are more effective than work equivalent nodal forces in cases where the loading is mainly carried by membrane forces and coarse meshes are used. The performance of the proposed element is compared with state-of-the-art elements, known from the literature.

Efficient Kriging-based robust optimization of unconstrained problems

Abstract A novel methodology, based on Kriging and expected improvement, is proposed for applying robust optimization on unconstrained problems affected by implementation error. A modified expected improvement measure which reflects the need for robust instead of nominal optimization is used to provide new sampling point locations. A new sample is added at each iteration by finding the location at which the modified expected improvement measure is maximum. By means of this process, the algorithm iteratively progresses towards the robust optimum. It is demonstrated that the algorithm performs significantly better than current techniques for robust optimization using response surface modeling.