A time-domain method for the analysis of thermal impedance response preserving the convolution form

The study of the thermal behavior of complex packages as multichip modules (MCM¿s) is usually carried out by measuring the so-called thermal impedance response, that is: the transient temperature after a power step. From the analysis of this signal, the thermal frequency response can be estimated, and consequently, compact thermal models may be extracted. We present a method to obtain an estimate of the time constant distribution underlying the observed transient. The method is based on an iterative deconvolution that produces an approximation to the time constant spectrum while preserving a convenient convolution form. This method is applied to the obtained thermal response of a microstructure as analyzed by finite element method as well as to the measured thermal response of a transistor array integrated circuit (IC) in a SMD package.

A multilevel multiscale finite volume method

The Multiscale Finite Volume (MsFV) method has been developed to efficiently solve reservoir-scale problems while conserving fine-scale details. The method employs two grid levels: a fine grid and a coarse grid. The latter is used to calculate a coarse solution to the original problem, which is interpolated to the fine mesh. The coarse system is constructed from the fine-scale problem using restriction and prolongation operators that are obtained by introducing appropriate localization assumptions. Through a successive reconstruction step, the MsFV method is able to provide an approximate, but fully conservative fine-scale velocity field. For very large problems (e.g. one billion cell model), a two-level algorithm can remain computational expensive. Depending on the upscaling factor, the computational expense comes either from the costs associated with the solution of the coarse problem or from the construction of the local interpolators (basis functions). To ensure numerical efficiency in the former case, the MsFV concept can be reapplied to the coarse problem, leading to a new, coarser level of discretization. One challenge in the use of a multilevel MsFV technique is to find an efficient reconstruction step to obtain a conservative fine-scale velocity field. In this work, we introduce a three-level Multiscale Finite Volume method (MlMsFV) and give a detailed description of the reconstruction step. Complexity analyses of the original MsFV method and the new MlMsFV method are discussed, and their performances in terms of accuracy and efficiency are compared.

Importance of polyethylene thickness in total shoulder arthroplasty: a finite element analysis.

BACKGROUND: Articular surfaces reconstruction is essential in total shoulder arthroplasty. Because of the limited glenoid bone support, thin glenoid component could improve anatomical reconstruction, but adverse mechanical effects might appear. METHODS: With a numerical musculoskeletal shoulder model, we analysed and compared three values of thickness of a typical all-polyethylene glenoid component: 2, 4 (reference) and 6mm. A loaded movement of abduction in the scapular plane was simulated. We evaluated the humeral head translation, the muscle moment arms, the joint force, the articular contact pattern, and the polyethylene and cement stress. Findings Decreasing polyethylene thickness from 6 to 2mm slightly increased humeral head translation and muscle moment arms. This induced a small decreased of the joint reaction force, but important increase of stress within the polyethylene and the cement mantel. Interpretation The reference thickness of 4mm seems a good compromise to avoid stress concentration and joint stuffing.

Nonlinear Finite Element Study of Piles in Integral Abutment Bridges, HR-227, Part 2, 1982

The highway departments of the states which use integral abutments in bridge design were contacted in order to study the extent of integral abutment use in skewed bridges and to survey the different guidelines used for analysis and design of integral abutments in skewed bridges. The variation in design assumptions and pile orientations among the various states in their approach to the use of integral abutments on skewed bridges is discussed. The problems associated with the treatment of the approach slab, backfill, and pile cap, and the reason for using different pile orientations are summarized in the report. An algorithm based on a state-of-the-art nonlinear finite element procedure previously developed by the authors was modified and used to study the influence of different factors on behavior of piles in integral abutment bridges. An idealized integral abutment was introduced by assuming that the pile is rigidly cast into the pile cap and that the approach slab offers no resistance to lateral thermal expansion. Passive soil and shear resistance of the cap are neglected in design. A 40-foot H pile (HP 10 X 42) in six typical Iowa soils was analyzed for fully restrained pile head and pinned pile head. According to numerical results, the maximum safe length for fully restrained pile head is one-half the maximum safe length for pinned pile head. If the pile head is partially restrained, the maximum safe length will lie between the two limits. The numerical results from an investigation of the effect of predrilled oversized holes indicate that if the length of the predrilled oversized hole is at least 4 feet below the ground, the vertical load-carrying capacity of the H pile is only reduced by 10 percent for 4 inches of lateral displacement in very stiff clay. With no predrilled oversized hole, the pile failed before the 4-inch lateral displacement was reached. Thus, the maximum safe lengths for integral abutment bridges may be increased by predrilling. Four different typical Iowa layered soils were selected and used in this investigation. In certain situations, compacted soil (> 50 blow count in standard penetration tests) is used as fill on top of natural soil. The numerical results showed that the critical conditions will depend on the length of the compacted soil. If the length of the compacted soil exceeds 4 feet, the failure mechanism for the pile is similar to one in a layer of very stiff clay. That is, the vertical load-carrying capacity of the H pile will be greatly reduced as the specified lateral displacement increases.

An operator formulation of the multiscale finite-volume method with correction function

The multiscale finite-volume (MSFV) method has been derived to efficiently solve large problems with spatially varying coefficients. The fine-scale problem is subdivided into local problems that can be solved separately and are coupled by a global problem. This algorithm, in consequence, shares some characteristics with two-level domain decomposition (DD) methods. However, the MSFV algorithm is different in that it incorporates a flux reconstruction step, which delivers a fine-scale mass conservative flux field without the need for iterating. This is achieved by the use of two overlapping coarse grids. The recently introduced correction function allows for a consistent handling of source terms, which makes the MSFV method a flexible algorithm that is applicable to a wide spectrum of problems. It is demonstrated that the MSFV operator, used to compute an approximate pressure solution, can be equivalently constructed by writing the Schur complement with a tangential approximation of a single-cell overlapping grid and incorporation of appropriate coarse-scale mass-balance equations.

Effective notch method assessment of misalignment for fatigue loaded welds

 The objective of this thesis work was to assess axial misalignment in fatigue loaded welds using the effective notch method. As a result, the fatigue behaviour of non-load carrying cruciform fillet welded joint under cyclic tensile loading has been studied. Various degrees of axial misalignment have been found in one series of non-load carrying cruciform fillet welded joints used in a laboratory investigation. As a result, it was important to carry out a comprehensive investigation since axial misalignment forms part of thequality of fatigue loaded structure and can reduce the fatigue strength. To extend the study, the correlation between fatigue strength and stress ratio, as well as stress concentration factor, were also studied. Moreover, a closer investigation of place of crack initiation and its dependence on weld sequence and imperfections of test specimen (angular distortion) was studied. For the fatigue class calculations, FEM (finite element method) and the effectivenotch approach are used. The addressed variable is the axial misalignment whichis introduce by modeling the entire joint. Fracture mechanics based calculations are also used and quantitatively compared with effective notch and experimental results.

Analysis of a finite volume method for a cross-diffusion model in population dynamics

The main goal of this paper is to propose a convergent finite volume method for a reactionâeuro"diffusion system with cross-diffusion. First, we sketch an existence proof for a class of cross-diffusion systems. Then the standard two-point finite volume fluxes are used in combination with a nonlinear positivity-preserving approximation of the cross-diffusion coefficients. Existence and uniqueness of the approximate solution are addressed, and it is also shown that the scheme converges to the corresponding weak solution for the studied model. Furthermore, we provide a stability analysis to study pattern-formation phenomena, and we perform two-dimensional numerical examples which exhibit formation of nonuniform spatial patterns. From the simulations it is also found that experimental rates of convergence are slightly below second order. The convergence proof uses two ingredients of interest for various applications, namely the discrete Sobolev embedding inequalities with general boundary conditions and a space-time $L^1$ compactness argument that mimics the compactness lemma due to Kruzhkov. The proofs of these results are given in the Appendix.

Finite Element Analysis of Electrically Excited Quartz Tuning Fork Devices

Quartz Tuning Fork (QTF)-based Scanning Probe Microscopy (SPM) is an important field of research. A suitable model for the QTF is important to obtain quantitative measurements with these devices. Analytical models have the limitation of being based on the double cantilever configuration. In this paper, we present an electromechanical finite element model of the QTF electrically excited with two free prongs. The model goes beyond the state-of-the-art of numerical simulations currently found in the literature for this QTF configuration. We present the first numerical analysis of both the electrical and mechanical behavior of QTF devices. Experimental measurements obtained with 10 units of the same model of QTF validate the finite element model with a good agreement.

Effect of partial-thickness tear on loading capacities of the supraspinatus tendon: a finite element analysis.

Partial-thickness tears of the supraspinatus tendon frequently occur at its insertion on the greater tubercule of the humerus, causing pain and reduced strength and range of motion. The goal of this work was to quantify the loss of loading capacity due to tendon tears at the insertion area. A finite element model of the supraspinatus tendon was developed using in vivo magnetic resonance images data. The tendon was represented by an anisotropic hyperelastic constitutive law identified with experimental measurements. A failure criterion was proposed and calibrated with experimental data. A partial-thickness tear was gradually increased, starting from the deep articular-sided fibres. For different values of tendon tear thickness, the tendon was mechanically loaded up to failure. The numerical model predicted a loss in loading capacity of the tendon as the tear thickness progressed. Tendon failure was more likely when the tendon tear exceeded 20%. The predictions of the model were consistent with experimental studies. Partial-thickness tears below 40% tear are sufficiently stable to persist physiotherapeutic exercises. Above 60% tear surgery should be considered to restore shoulder strength.

Impact of the Femoral Head Position on Moment Arms in Total Hip Arthroplasty: A Parametric Finite Element Study.

BACKGROUND: Although the importance of accurate femoral reconstruction to achieve a good functional outcome is well documented, quantitative data on the effects of a displacement of the femoral center of rotation on moment arms are scarce. The purpose of this study was to calculate moment arms after nonanatomical femoral reconstruction. METHODS: Finite element models of 15 patients including the pelvis, the femur, and the gluteal muscles were developed. Moment arms were calculated within the native anatomy and compared to distinct displacement of the femoral center of rotation (leg lengthening of 10 mm, loss of femoral offset of 20%, anteversion ±10°, and fixed anteversion at 15°). Calculations were performed within the range of motion observed during a normal gait cycle. RESULTS: Although with all evaluated displacements of the femoral center of rotation, the abductor moment arm remained positive, some fibers initially contributing to extension became antagonists (flexors) and vice versa. A loss of 20% of femoral offset led to an average decrease of 15% of abductor moment. Femoral lengthening and changes in femoral anteversion (±10°, fixed at 15°) led to minimal changes in abductor moment arms (maximum change of 5%). Native femoral anteversion correlated with the changes in moment arms induced by the 5 variations of reconstruction. CONCLUSION: Accurate reconstruction of offset is important to maintaining abductor moment arms, while changes of femoral rotation had minimal effects. Patients with larger native femoral anteversion appear to be more susceptible to femoral head displacements.

Be-Fe coupled method for the analysis of 3D elastodynamic problems in the time domain

By coupling the Boundary Element Method (BEM) and the Finite Element Method (FEM) an algorithm that combines the advantages of both numerical processes is developed. The main aim of the work concerns the time domain analysis of general three-dimensional wave propagation problems in elastic media. In addition, mathematical and numerical aspects of the related BE-, FE- and BE/FE-formulations are discussed. The coupling algorithm allows investigations of elastodynamic problems with a BE- and a FE-subdomain. In order to observe the performance of the coupling algorithm two problems are solved and their results compared to other numerical solutions.

Contact with friction using the augmented Lagrangian Method: a conditional constrained minimization problem

This work presents a formulation of the contact with friction between elastic bodies. This is a non linear problem due to unilateral constraints (inter-penetration of bodies) and friction. The solution of this problem can be found using optimization concepts, modelling the problem as a constrained minimization problem. The Finite Element Method is used to construct approximation spaces. The minimization problem has the total potential energy of the elastic bodies as the objective function, the non-inter-penetration conditions are represented by inequality constraints, and equality constraints are used to deal with the friction. Due to the presence of two friction conditions (stick and slip), specific equality constraints are present or not according to the current condition. Since the Coulomb friction condition depends on the normal and tangential contact stresses related to the constraints of the problem, it is devised a conditional dependent constrained minimization problem. An Augmented Lagrangian Method for constrained minimization is employed to solve this problem. This method, when applied to a contact problem, presents Lagrange Multipliers which have the physical meaning of contact forces. This fact allows to check the friction condition at each iteration. These concepts make possible to devise a computational scheme which lead to good numerical results.