Meshless Local Petrov-Galerkin (MLPG) Method with Orthogonal Polynomials for Euler-Bernoulli Beam Problems

In this paper, the feasibility of orthogonal polynomials in the meshless local Petrov Galerkin method (MLPG) method is studied. The orthogonal polynomials, Chebyshev and Legendre polynomials, are used in this MLPG method as trial functions. The test functions used were power functions with smooth derivatives at their ends. The performance of these methods is studied by applying these methods to Euler-Bernoulli beam problems. The MLPG-Galerkin and Legendre methods passed all the patch tests for simple beam problems. Next the formulations are tested on complex beam problems such as beams with partial loadings and continuous beam problems. Problems with load discontinuities and additional supports require special attention. Near discontinuities, judicious choice of number of nodes and nodal placements are needed to obtain accurate deflections, slopes, moments and shear forces. As polynomial functions are used, the large number of nodes can create a transformation matrix that is ill-conditioned, resulting in problems with the inversion of the matrix. The conditioning worsens as the number of nodes are increased beyond 20. Quadruple precision was needed for models to obtain accurate solutions. Even with quadruple precision the accuracy of the method suffers as the number of nodes is increased beyond 20. This appears to be a drawback of the MLPG-Chebyshev and MLPG-Legendre methods

Panamerican Trauma Society: The first three decades

Panamerican Trauma Society was born 30 years ago with the mission of improving trauma care in the Americas by exchange of ideas and concepts and expanding knowledge of trauma and acute illness. The authors, immediate-past leaders of the organization, review the evolution of this assembly of diverse cultures and nationalities

Simple Test Functions in Meshless Local Petrov-Galerkin Methods

Two meshless local Petrov-Galerkin (MLPG) methods based on two different trial functions but that use a simple linear test function were developed for beam and column problems. These methods used generalized moving least squares (GMLS) and radial basis (RB) interpolation functions as trial functions. These two methods were tested on various patch test problems. Both methods passed the patch tests successfully. Then the methods were applied to various beam vibration problems and problems involving Euler and Beck's columns. Both methods yielded accurate solutions for all problems studied. The simple linear test function offers considerable savings in computing efforts as the domain integrals involved in the weak form are avoided. The two methods based on this simple linear test function method produced accurate results for frequencies and buckling loads. Of the two methods studied, the method with radial basis trial functions is very attractive as the method is simple, accurate, and robust

Use of Simple Continuum Solutions in Finite Element Alternating Method for Fracture Problems

The performance of the finite element alternating (FEAM) method for two-dimensional crack problems is studied with respect to a polynomial pressure distribution fitted to the crack face stresses. The FEAM alternates between the analytical solution of crack in an infinite plate subjected to arbitrary polynomial distribution and a finite element solution of an uncracked body to satisfy the required boundary conditions in the crack problem. In this paper, the FEAM is applied to embedded crack and edge crack problems. For embedded crack problems, all of the constant, linear, and quadratic ( N=0,1, or 2, respectively) pressure distributions yield very accurate results with this algorithm with 4 to 5 iterations. The edge crack problems, on the other hand, require much higher order polynomials distributions (N=5 to 6) to yield accurate solutions. For slant edge crack problems, the mode-I stress-intensity factors have better accuracy than the mode-II stress-intensity factors for the same convergence tolerance

Fracture Mechanics Analyses for Interface Crack Problems - A Review

Recent developments in fracture mechanics analyses of the interfacial crack problem are reviewed. The intent of the review is to renew the awareness of the oscillatory singularity at the crack tip of a bimaterial interface and the problems that occur when calculating mode mixity using numerical methods such as the finite element method in conjunction with the virtual crack closure technique. Established approaches to overcome the nonconvergence issue of the individual mode strain energy release rates are reviewed. In the recent literature many attempts to overcome the nonconvergence issue have been developed. Among the many approaches found only a few methods hold the promise of providing practical solutions. These are the resin interlayer method, the method that chooses the crack tip element size greater than the oscillation zone, the crack tip element method that is based on plate theory and the crack surface displacement extrapolation method. Each of the methods is validated on a very limited set of simple interface crack problems. However, their utility for a wide range of interfacial crack problems is yet to be established

Negative Stress Margins - Are They Real?

Advances in modeling and simulation, new finite element software, modeling engines and powerful computers are providing opportunities to interrogate designs in a very different manner and in a more detailed approach than ever before. Margins of safety are also often evaluated using local stresses for various design concepts and design parameters quickly once analysis models are defined and developed. This paper suggests that not all the negative margins of safety evaluated are real. The structural areas where negative margins are frequently encountered are often near stress concentrations, point loads and load discontinuities, near locations of stress singularities, in areas having large gradients but with insufficient mesh density, in areas with modeling issues and modeling errors, and in areas with connections and interfaces, in two-dimensional (2D) and three-dimensional (3D) transitions, bolts and bolt modeling, and boundary conditions. Now, more than ever, structural analysts need to examine and interrogate their analysis results and perform basic sanity checks to determine if these negative margins are real

Weld Residual Stress and Distortion Analysis of the ARES I-X Upper Stage Simulator (USS)

An independent assessment was conducted to determine the critical initial flaw size (CIFS) for the flange-to-skin weld in the Ares I-X Upper Stage Simulator (USS). The Ares system of space launch vehicles is the US National Aeronautics and Space Administration s plan for replacement of the aging space shuttle. The new Ares space launch system is somewhat of a combination of the space shuttle system and the Saturn launch vehicles used prior to the shuttle. Here, a series of weld analyses are performed to determine the residual stresses in a critical region of the USS. Weld residual stresses both increase constraint and mean stress thereby having an important effect on fatigue and fracture life. While the main focus of this paper is a discussion of the weld modeling procedures and results for the USS, a short summary of the CIFS assessment is provided

Fracture Mechanics Analyses of Subsurface Defects in Reinforced Carbon-Carbon Joggles Subjected to Thermo-Mechanical Loads

Coating spallation events have been observed along the slip-side joggle region of the Space Shuttle Orbiter wing-leading-edge panels. One potential contributor to the spallation event is a pressure build up within subsurface voids or defects due to volatiles or water vapor entrapped during fabrication, refurbishment, or normal operational use. The influence of entrapped pressure on the thermo-mechanical fracture-mechanics response of reinforced carbon-carbon with subsurface defects is studied. Plane-strain simulations with embedded subsurface defects are performed to characterize the fracture mechanics response for a given defect length when subjected to combined elevated-temperature and subsurface-defect pressure loadings to simulate the unvented defect condition. Various subsurface defect locations of a fixed-length substrate defect are examined for elevated temperature conditions. Fracture mechanics results suggest that entrapped pressure combined with local elevated temperatures have the potential to cause subsurface defect growth and possibly contribute to further material separation or even spallation. For this anomaly to occur, several unusual circumstances would be required making such an outcome unlikely but plausible

Contributing Factors to Postoperative Length of Stay in Laparoscopic Cholecystectomy

This study indicates that patients undergoing laparoscopic cholecystectomy have discernable characteristics that can contribute in a major way to postoperative length of stay

Stress Analysis of Bolted, Segmented Cylindrical Shells Exhibiting Flange Mating-Surface Waviness

Bolted, segmented cylindrical shells are a common structural component in many engineering systems especially for aerospace launch vehicles. Segmented shells are often needed due to limitations of manufacturing capabilities or transportation issues related to very long, large-diameter cylindrical shells. These cylindrical shells typically have a flange or ring welded to opposite ends so that shell segments can be mated together and bolted to form a larger structural system. As the diameter of these shells increases, maintaining strict fabrication tolerances for the flanges to be flat and parallel on a welded structure is an extreme challenge. Local fit-up stresses develop in the structure due to flange mating-surface mismatch (flange waviness). These local stresses need to be considered when predicting a critical initial flaw size. Flange waviness is one contributor to the fit-up stress state. The present paper describes the modeling and analysis effort to simulate fit-up stresses due to flange waviness in a typical bolted, segmented cylindrical shell. Results from parametric studies are presented for various flange mating-surface waviness distributions and amplitudes