T. Krishnamurthy

Optimized Vertex Method and Hybrid Reliability

A method of calculating the fuzzy response of a system is presented. This method, called the Optimized Vertex Method (OVM), is based upon the vertex method but requires considerably fewer function evaluations. The method is demonstrated by calculating the response membership function of strain-energy release rate for a bonded joint with a crack. The possibility of failure of the bonded joint was determined over a range of loads. After completing the possibilistic analysis, the possibilistic (fuzzy) membership functions were transformed to probability density functions and the probability of failure of the bonded joint was calculated. This approach is called a possibility-based hybrid reliability assessment. The possibility and probability of failure are presented and compared to a Monte Carlo Simulation (MCS) of the bonded joint.

Probabilistic Design of a Plate-Like Wing to Meet Flutter and Strength Requirements

An approach is presented for carrying out reliability-based design of a metallic, plate-like wing to meet strength and flutter requirements that are given in terms of risk/reliability. The design problem is to determine the thickness distribution such that wing weight is a minimum and the probability of failure is less than a specified value. Failure is assumed to occur if either the flutter speed is less than a specified allowable or the stress caused by a pressure loading is greater than a specified allowable. Four uncertain quantities are considered: wing thickness, calculated flutter speed, allowable stress, and magnitude of a uniform pressure load.

Equivalent Plate Analysis of Aircraft Wing with Discrete Source Damage

An equivalent plate procedure is developed to provide a computationally efficient means of matching the stiffness and frequencies of flight vehicle wing structures for prescribed loading conditions. First, the equivalent plate is used to match the stiffness of a stiffened panel without damage and the stiffness of a stiffened panel with damage. For both stiffened panels, the equivalent plate models reproduce the deformation of a corresponding detailed model exactly for the given loading conditions. Once the stiffness was matched, the equivalent plate models were then used to predict the frequencies of the panels. Two analytical procedures using the lumped-mass matrix were used to match the first five frequencies of the corresponding detailed model. In both the procedures, the lumped-mass matrix for the equivalent plate is constructed by multiplying the diagonal terms of the consistent-mass matrix by a proportionality constant. In the first procedure, the proportionality constant is selected such that the total mass of the equivalent plate is equal to that of the detailed model. In the second method, the proportionality constant is selected to minimize the sum of the squares of the errors in a set of pre-selected frequencies between the equivalent plate model and the detailed model. The equivalent plate models reproduced the fundamental first frequency accurately in both the methods. It is observed that changing only the mass distribution in the equivalent plate model did not provide enough flexibility to match all of the frequencies.

Probabilistic Design of a Wind Tunnel Model to Match the Response of a Full-Scale Aircraft

An approach is presented for carrying out the reliability-based design of a plate-like wing that is part of a wind tunnel model. The goal is to design the wind tunnel model to match the stiffness characteristics of the wing box of a flight vehicle while satisfying strength-based risk/reliability requirements that prevents damage to the wind tunnel model and fixtures. The flight vehicle is a modified F/A-18 aircraft. The design problem is solved using reliability-based optimization techniques. The objective function to be minimized is the difference between the displacements of the wind tunnel model and the corresponding displacements of the flight vehicle. The design variables control the thickness distribution of the wind tunnel model. Displacements of the wind tunnel model change with the thickness distribution, while displacements of the flight vehicle are a set of fixed data. The only constraint imposed is that the probability of failure is less than a specified value. Failure is assumed to occur if the stress caused by aerodynamic pressure loading is greater than the specified strength allowable. Two uncertain quantities are considered: the allowable stress and the thickness distribution of the wind tunnel model. Reliability is calculated using Monte Carlo simulation with response surfaces that provide approximate values of stresses. The response surface equations are, in turn, computed from finite element analyses of the wind tunnel model at specified design points. Because the response surface approximations were fit over a small region centered about the current design, the response surfaces were refit periodically as the design variables changed. Coarse-grained parallelism was used to simultaneously perform multiple finite element analyses. Studies carried out in this paper demonstrate that this scheme of using moving response surfaces and coarse-grained computational parallelism reduce the execution time of the Monte Carlo simulation enough to make the design problem tractable. The results of the reliability-based designs performed in this paper show that large decreases in the probability of stress-based failure can be realized with only small sacrifices in the ability of the wind tunnel model to represent the displacements of the full-scale vehicle.

NASA Structural Analysis Report on the American Airlines Flight 587 Accident- Local Analysis of the Right Rear Lug

A detailed finite element analysis of the right rear lug of the American Airlines Flight 587 - Airbus A300-600R was performed as part of the National Transportation Safety Board’s failure investigation of the accident that occurred on November 12, 2001. The loads experienced by the right rear lug are evaluated using global models of the vertical tail, local models near the right rear lug, and a global -local analysis procedure. The right rear lug was analyzed using two modeling approaches. In the first approach, solid-shell type modeling is used, and in the second approach, layered-shell type modeling is used. The solid-shell and the layered-shell modeling approaches were used in progressive failure analyses (PFA) to determine the load, mode, and location of failure in the right rear lug under loading representative of an Airbus certification test conducted in 1985 (the 1985-certification test). Both analyses were in excellent agreement with each other on the predicted failure loads, failure mode, and location of failure. The solid-shell type modeling was then used to analyze both a subcomponent test conducted by Airbus in 2003 (the 2003-subcomponent test) and the accident condition. Excellent agreement was observed between the analyses and the observed failures in both cases. From the analyses conducted and presented in this paper, the following conclusions were drawn. The moment, Mx (moment about the fuselage longitudinal axis), has significant effect on the failure load of the lugs. Higher absolute values of Mx give lower failure loads. The predicted load, mode, and location of the failure of the 1985-certification test, 2003-subcomponent test, and the accident condition are in very good agreement. This agreement suggests that the 1985-certification and 2003subcomponent tests represent the accident condition accurately. The failure mode of the right rear lug for the 1985-certification test, 2003-subcomponent test, and the accident load case is identified as a cleavage-type failure. For the accident case, the predicted failure load for the right rear lug from the PFA is greater than 1.98 times the limit load of the lugs.

Meshless Local Petrov-Galerkin Euler-Bernoulli Beam Problems: A Radial Basis Function Approach

A radial basis function implementation of the meshless local Petrov-Galerkin (MLPG) method is presented to study Euler-Bernoulli beam problems. Radial basis functions, rather than generalized moving least squares (GMLS) interpolations, are used to develop the trial functions. This choice yields a computationally simpler method as fewer matrix inversions and multiplications are required than when GMLS interpolations are used. Test functions are chosen as simple weight functions as in the conventional MLPG method. Compactly and noncompactly supported radial basis functions are considered. The non-compactly supported cubic radial basis function is found to perform very well. Results obtained from the radial basis MLPG method are comparable to those obtained using the conventional MLPG method for mixed boundary value problems and problems with discontinuous loading conditions.

Probabilistic Analysis of a Composite Crew Module

An approach for conducting reliability-based analys is (RBA) of a Composite Crew Module (CCM) is presented. The goal is to identify and quantify the benefits of probabilistic design methods for the CCM and future space vehicles. The coarse finite element model from a previous NASA Engineering and Safety Center (NESC) project is used as the baseline deterministic analysis model to evaluate t he performance of the CCM using a strength-based failure index. The first step in th e probabilistic analysis process is the determination of the uncertainty distributions for key parameters in the model. Analytical data from water landing simulations are used to dev elop an uncertainty distribution, but such data were unavailable for other load cases. T he uncertainty distributions for the other load scale factors and the strength allowables are generated based on assumed coefficients of variation. Probability of first-ply failure is est imated using three methods: the first order reliability method (FORM), Monte Carlo simulation, and conditional sampling. Results for the three methods were consistent. The reliability is shown to be driven by first ply failure in one region of the CCM at the high altitude abort load set. The final predicted probability of failure is on the order of 10 -11 due to the conservative nature of the factors of s afety on the deterministic loads. I. Introduction A. Motivation and Background A probabilistic approach is an attractive alternati ve to traditional deterministic design optimization by quantifying the level of safety (i.e. reliability) of a structure instead of a simple safe/unsafe eval uation. Probabilistic analysis and optimization can result in improved de signs considering the variability of structural mat erials and the uncertainty in loads. Traditional deterministic de sign relies on historically or arbitrarily assigned factors of safety to account for uncertainties in the design. These fac tors of safety are believed to reduce the probabili ty of mission failure to very low levels (e.g. 10 -7 or lower probability of failure) in commercial avi ation. However, NASA’s space flight program has a higher tolerance for risk (and a much higher sensitivity to mass savings) than co mmercial aviation. Probabilistic methods potentially enable the designer to trade off risk for increased mass savings, which is of great benefit to the space flight program. In early 2010, the NASA Engineering and Safety Center (NESC) initiated a Probabilistic Design Opportun ity Identification (PDOI) task to illustrate the advant ages of probabilistic design. The PDOI team select ed the Composite Crew Module (CCM) as a design problem due to its large amount of data available for structur al geometry, loads, and material models from the NESC’s recently completed design, development, test and evaluation (DDT&E) project. The CCM (Ref. 1) is a concept six crew space vehicle similar to the Orion project’s Crew Exploration Vehicle (CEV), except the CCM is manufactured using composite materials and design techniq ues. Results from this CCM study will be used to help es tablish probabilistic analysis as a design tool for future projects within NASA and to help establish probabilistic des ign requirements as an alternative to traditional f actor of safety requirements. In this paper, results are presented from phase 1 of the project, which includes reliab ility calculations for the baseline CCM design. B. Purpose and Contents The purpose of this CCM design study is to answer i mportant questions about applying reliability-based design and optimization (RBDO) to spacecraft design in general and, more specifically, to the design of the C CM. First, does the probabilistic approach require exorbitant computer resources or measured data that are unavai lable? This question is answered by estimating the computational costs of probabilistic analysis and establishing the needed and available data for the CCM. Next, what is the base line reliability of the CCM and what parameters hav e the greatest effect on reliability? Monte Carlo simulation and first order reliability methods (FORM) are used to answer this

Use of Simple Continuum Solutions in Finite Element Alternating Method (FEAM) 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 ( 0,1, or 2 N  , 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. Introduction Stress-intensity factors are fundamental parameters to predict fracture strength and fatigue life of structural components. Several methods are available in the literature to estimate the stressintensity factors of cracked structural components. Several well-documented stress-intensity factor handbooks [1-4] are also available. However, for many structural components and loading conditions, the stress-intensity factors are not readily available. Finite Element Method (FEM) is the most widely used method to calculate the stress-intensity factors for complicated crack geometries. FE methods to estimate the stress-intensity factors without actually modeling the crack configurations are very attractive. The literature shows that the Finite Element Alternating Method (FEAM) is a powerful and efficient method [5] to estimate the stress-intensity factors in three[5,6] and two-dimensional [7,8] structural components without actually modeling the crack configuration. The FEAM uses two solutions to solve the fracture mechanics problem. The first solution is a numerical solution such as FEM to analyze the uncracked body subjected to the same loading conditions as the original crack problem and the second solution is a basic continuum solution (also referred to as analytical solution in this paper) for a cracked infinite plate or solid (see Figure 1). The FEAM is based on the Schwartz-Neumann alternating method [4-8] and alternates between two solutions, FEM and continuum to satisfy the boundary conditions of the problem [5-8]. The iterations are continued until the required level of accuracy is achieved. The continuum solution is an exact elasticity solution for a crack in an infinite plate subjected to arbitrary polynomial tractions at the crack faces. The normal and tangential tractions, p , on the crack faces are assumed to be of a general polynomial form [7,8]. For the finite element part of the method, the structural component is modeled without modeling the crack, and analyzed for the given applied loading and boundary conditions. Since there are no singularities modeled in https://ntrs.nasa.gov/search.jsp?R=20180006192 2019-06-06T10:22:55+00:00Z