Integrated force method versus displacement method for finite element analysis

A novel formulation termed the integrated force method (IFM) has been developed in recent years for analyzing structures. In this method all the internal forces are taken as independent variables, and the system equilibrium equations (EE's) are integrated with the global compatibility conditions (CC's) to form the governing set of equations. In IFM the CC's are obtained from the strain formulation of St. Venant, and no choices of redundant load systems have to be made, in constrast to the standard force method (SFM). This property of IFM allows the generation of the governing equation to be automated straightforwardly, as it is in the popular stiffness method (SM). In this report IFM and SM are compared relative to the structure of their respective equations, their conditioning, required solution methods, overall computational requirements, and convergence properties as these factors influence the accuracy of the results. Overall, this new version of the force method produces more accurate results than the stiffness method for comparable computational cost

Compatibility conditions of structural mechanics for finite element analysis

The equilibrium equations and the compatibility conditions are fundamental to the analyses of structures. However, anyone who undertakes even a cursory generic study of the compatibility conditions can discover, with little effort, that historically this facet of structural mechanics had not been adequately researched by the profession. Now the compatibility conditions (CC's) have been researched and are understood to a great extent. For finite element discretizations, the CC's are banded and can be divided into three distinct categories: (1) the interface CC's; (2) the cluster or field CC's; and (3) the external CC's. The generation of CC's requires the separating of a local region, then writing the deformation displacement relation (ddr) for the region, and finally, the eliminating of the displacements from the ddr. The procedure to generate all three types of CC's is presented and illustrated through examples of finite element models. The uniqueness of the CC's thus generated is shown

Singularities in optimal structural design

Singularity conditions that arise during structural optimization can seriously degrade the performance of the optimizer. The singularities are intrinsic to the formulation of the structural optimization problem and are not associated with the method of analysis. Certain conditions that give rise to singularities have been identified in earlier papers, encompassing the entire structure. Further examination revealed more complex sets of conditions in which singularities occur. Some of these singularities are local in nature, being associated with only a segment of the structure. Moreover, the likelihood that one of these local singularities may arise during an optimization procedure can be much greater than that of the global singularity identified earlier. Examples are provided of these additional forms of singularities. A framework is also given in which these singularities can be recognized. In particular, the singularities can be identified by examination of the stress displacement relations along with the compatibility conditions and/or the displacement stress relations derived in the integrated force method of structural analysis

MERLIN/VLA imaging of the gravitational lens system B0218+357

Gravitational lenses offer the possibility of accurately determining the Hubble parameter (H_0) over cosmological distances, and B0218+357 is one of the most promising systems for an application of this technique. In particular this system has an accurately measured time delay (10.5+/-0.4 d; Biggs et al. 1999) and preliminary mass modelling has given a value for H_0 of 69 +13/-19 km/s/Mpc. The error on this estimate is now dominated by the uncertainty in the mass modelling. As this system contains an Einstein ring it should be possible to constrain the model better by imaging the ring at high resolution. To achieve this we have combined data from MERLIN and the VLA at a frequency of 5 GHz. In particular MERLIN has been used in multi-frequency mode in order to improve substantially the aperture coverage of the combined data set. The resulting map is the best that has been made of the ring and contains many new and interesting features. Efforts are currently underway to exploit the new data for lensing constraints using the LensClean algorithm (Kochanek & Narayan 1992).Comment: Accepted for publication in MNRAS. 6 pages, 4 included PostScript figure

Strong lensing constraints on the velocity dispersion and density profile of elliptical galaxies

We use the statistics of strong gravitational lensing from the CLASS survey to impose constraints on the velocity dispersion and density profile of elliptical galaxies. This approach differs from much recent work, where the luminosity function, velocity dispersion and density profile were typically {\it assumed} in order to constrain cosmological parameters. It is indeed remarkable that observational cosmology has reached the point where we can consider using cosmology to constrain astrophysics, rather than vice versa. We use two different observables to obtain our constraints (total optical depth and angular distributions of lensing events). In spite of the relatively poor statistics and the uncertain identification of lenses in the survey, we obtain interesting constraints on the velocity dispersion and density profiles of elliptical galaxies. For example, assuming the SIS density profile and marginalizing over other relevant parameters, we find 168 km/s < sigma_* < 200 km/s (68% CL), and 158 km/s < sigma_* < 220 km/s (95% CL). Furthermore, if we instead assume a generalized NFW density profile and marginalize over other parameters, the slope of the profile is constrained to be 1.50 < beta < 2.00 (95% CL). We also constrain the concentration parameter as a function of the density profile slope in these models. These results are essentially independent of the exact knowledge of cosmology. We briefly discuss the possible impact on these constraints of allowing the galaxy luminosity function to evolve with redshift, and also possible useful future directions for exploration.Comment: Uses the final JVAS/CLASS sample, more careful choice of ellipticals, added discussion of possible biases. Final results essentially unchanged. Matches the MNRAS versio

Optimization Testbed Cometboards Extended into Stochastic Domain

COMparative Evaluation Testbed of Optimization and Analysis Routines for the Design of Structures (CometBoards) is a multidisciplinary design optimization software. It was originally developed for deterministic calculation. It has now been extended into the stochastic domain for structural design problems. For deterministic problems, CometBoards is introduced through its subproblem solution strategy as well as the approximation concept in optimization. In the stochastic domain, a design is formulated as a function of the risk or reliability. Optimum solution including the weight of a structure, is also obtained as a function of reliability. Weight versus reliability traced out an inverted-S-shaped graph. The center of the graph corresponded to 50 percent probability of success, or one failure in two samples. A heavy design with weight approaching infinity could be produced for a near-zero rate of failure that corresponded to unity for reliability. Weight can be reduced to a small value for the most failure-prone design with a compromised reliability approaching zero. The stochastic design optimization (SDO) capability for an industrial problem was obtained by combining three codes: MSC/Nastran code was the deterministic analysis tool, fast probabilistic integrator, or the FPI module of the NESSUS software, was the probabilistic calculator, and CometBoards became the optimizer. The SDO capability requires a finite element structural model, a material model, a load model, and a design model. The stochastic optimization concept is illustrated considering an academic example and a real-life airframe component made of metallic and composite materials

Interferometric Phase Calibration Sources in the Declination Range 0deg to -30deg

We present a catalog of 321 compact radio sources in the declination range 0deg > delta > -30deg. The positions of these sources have been measured with a two-dimensional rms accuracy of 35 milliarcseconds using the NRAO Very Large Array. Each source has a peak flux density >50 mJy at 8.4 GHz. We intend for this catalog to be used mainly for selection of phase calibration sources for radio interferometers, although compact radio sources have other scientific uses.Comment: 9 pages. To appear in ApJS. Catalog (Table 3) is abbreviated in printed version. Complete catalog available at ftp://ftp.aoc.nrao.edu/pub/staff/jwrobel/WPW2003_ApJS.tx