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

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

Ares I-X USS Material Testing

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). Material characterization tests were conducted to quantify the material behavior for use in the CIFS analyses. Fatigue crack growth rate, Charpy impact, and fracture tests were conducted on the parent and welded A516 Grade 70 steel. The crack growth rate tests confirmed that the material behaved in agreement with literature data and that a salt water environment would not significantly degrade the fatigue resistance. The Charpy impact tests confirmed that the fracture resistance of the material did not have a significant reduction for the expected operational temperatures of the vehicle

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

White Paper on Factors of Safety

Following the Columbia Accident Investigation Board (CAIB) Report, the "Diaz Team" identified CAIB Report elements with Agency-wide applicability. The "Diaz Report", A Renewed Commitment To Excellence, generated an action to "Review current policies and waivers on safety factors". This document addresses this action

Intra-abdominal hypertension and abdominal compartment syndrome in pancreatitis, paediatrics, and trauma

Intra-abdominal hypertension (IAH) is an important contributor to early organ dysfunction in trauma and sepsis. However, relatively little is known about the impact of intra-abdominal pressure (IAP) in general internal medicine, pregnant patients, and those with obesity or burns. The aim of this paper is to review the pathophysiologic implications and treatment options for IAH in these specific situations. A MEDLINE and PubMed search was performed and the resulting body-of-evidence included in the current review on the basis of relevance and scientific merit. There is increasing awareness of the role of IAH in different clinical situations. Specifically, IAH will develop in most (if not all) severely burned patients, and may contribute to early mortality. One should avoid over-resuscitation of these patients with large volumes of fluids, especially crystalloids. Acute elevations in IAP have similar effects in obese patients compared to non-obese patients, but the threshold IAP associated with organ dysfunction may be higher. Chronic elevations in IAP may, in part, be responsible for the pathogenesis of obesity-related co-morbid conditions such as hypertension, pseudotumor cerebri, pulmonary dysfunction, gastroesophageal reflux disease, and abdominal wall hernias. At the bedside, measuring IAP and considering IAH in all critical maternal conditions is essential, especially in preeclampsia/eclampsia where some have hypothesized that IAH may have an additional role. IAH in pregnancy must take into account the precautions for aorto-caval compression and has been associated with ovarian hyperstimulation syndrome. Recently, IAP has been associated with the cardiorenal dilemma and hepatorenal syndrome, and this has led to the recognition of the polycompartment syndrome. In conclusion, IAH and ACS have been associated with several patient populations beyond the classical ICU, surgical, and trauma patients. In all at risk conditions the focus should be on the early recognition of IAH and prevention of ACS. Patients at risk for IAH should be identified early through measurements of IAP. Appropriate actions should be taken when IAP increases above 15 mm Hg, especially if pressures reach above 20 mm Hg with new onset organ failure. Although non-operative measures come first, surgical decompression must not be delayed if these fail. Percutaneous drainage of ascites is a simple and potentially effective tool to reduce IAP if organ dysfunction develops, especially in burn patients. Escharotomy may also dramatically reduce IAP in the case of abdominal burns