Engineering topics

Nemeth, Michael P.

Publications and source records attributed to Nemeth, Michael P..

At least 19 records

NASA NTRS2014

Buckling Analysis for Stiffened Anisotropic Circular Cylinders Based on Sanders Nonlinear Shell Theory

Nonlinear and bifurcation buckling equations for elastic, stiffened, geometrically perfect, right-circular cylindrical, anisotropic shells subjected to combined loads are presented that are based on Sanders' shell theory. Based on these equations, a three-parameter approximate Rayleigh-Ritz solution and a classical solution to the buckling problem are presented for cylinders with simply supported edges. Extensive comparisons of results obtained from these solutions with published results are also presented for a wide range of cylinder constructions. These comparisons include laminated-composite cylinders with a wide variety of shell-wall orthotropies and anisotropies. Numerous results are also given that show the discrepancies between the results obtained by using Donnell's equations and variants of Sanders' equations. For some cases, nondimensional parameters are identified and "master" curves are presented that facilitate the concise representation of results.

Nemeth, Michael P.↗

NASA NTRS2013

A Leonard-Sanders-Budiansky-Koiter-Type Nonlinear Shell Theory with a Hierarchy of Transverse-Shearing Deformations

A detailed exposition on a refined nonlinear shell theory suitable for nonlinear buckling analyses of laminated-composite shell structures is presented. This shell theory includes the classical nonlinear shell theory attributed to Leonard, Sanders, Koiter, and Budiansky as an explicit proper subset. This approach is used in order to leverage the exisiting experience base and to make the theory attractive to industry. In addition, the formalism of general tensors is avoided in order to expose the details needed to fully understand and use the theory. The shell theory is based on "small" strains and "moderate" rotations, and no shell-thinness approximations are used. As a result, the strain-displacement relations are exact within the presumptions of "small" strains and "moderate" rotations. The effects of transverse-shearing deformations are included in the theory by using analyst-defined functions to describe the through-the-thickness distributions of transverse-shearing strains. Constitutive equations for laminated-composite shells are derived without using any shell-thinness approximations, and simplified forms and special cases are presented.

Nemeth, Michael P.↗

NASA NTRS2013

An Approximate Solution and Master Curves for Buckling of Symmetrically Laminated Composite Cylinders

Nondimensional linear-bifurcation buckling equations for balanced, symmetrically laminated cylinders with negligible shell-wall anisotropies and subjected to uniform axial compression loads are presented. These equations are solved exactly for the practical case of simply supported ends. Nondimensional quantities are used to characterize the buckling behavior that consist of a stiffness-weighted length-to-radius parameter, a stiffness-weighted shell-thinness parameter, a shell-wall nonhomogeneity parameter, two orthotropy parameters, and a nondimensional buckling load. Ranges for the nondimensional parameters are established that encompass a wide range of laminated-wall constructions and numerous generic plots of nondimensional buckling load versus a stiffness-weighted length-to-radius ratio are presented for various combinations of the other parameters. These plots are expected to include many practical cases of interest to designers. Additionally, these plots show how the parameter values affect the distribution and size of the festoons forming each response curve and how they affect the attenuation of each response curve to the corresponding solution for an infinitely long cylinder. To aid in preliminary design studies, approximate formulas for the nondimensional buckling load are derived, and validated against the corresponding exact solution, that give the attenuated buckling response of an infinitely long cylinder in terms of the nondimensional parameters presented herein. A relatively small number of "master curves" are identified that give a nondimensional measure of the buckling load of an infinitely long cylinder as a function of the orthotropy and wall inhomogeneity parameters. These curves reduce greatly the complexity of the design-variable space as compared to representations that use dimensional quantities as design variables. As a result of their inherent simplicity, these master curves are anticipated to be useful in the ongoing development of buckling-design technology.

Nemeth, Michael P.↗

NASA NTRS2013

An Exposition on the Nonlinear Kinematics of Shells, Including Transverse Shearing Deformations

An in-depth exposition on the nonlinear deformations of shells with "small" initial geometric imperfections, is presented without the use of tensors. First, the mathematical descriptions of an undeformed-shell reference surface, and its deformed image, are given in general nonorthogonal coordinates. The two-dimensional Green-Lagrange strains of the reference surface derived and simplified for the case of "small" strains. Linearized reference-surface strains, rotations, curvatures, and torsions are then derived and used to obtain the "small" Green-Lagrange strains in terms of linear deformation measures. Next, the geometry of the deformed shell is described mathematically and the "small" three-dimensional Green-Lagrange strains are given. The deformations of the shell and its reference surface are related by introducing a kinematic hypothesis that includes transverse shearing deformations and contains the classical Love-Kirchhoff kinematic hypothesis as a proper, explicit subset. Lastly, summaries of the essential equations are given for general nonorthogonal and orthogonal coordinates, and the basis for further simplification of the equations is discussed.

Nemeth, Michael P.↗

NASA NTRS2012

Conditions for Symmetries in the Buckle Patterns of Laminated-Composite Plates

Conditions for the existence of certain symmetries to exist in the buckle patterns of symmetrically laminated composite plates are presented. The plates considered have a general planform with cutouts, variable thickness and stiffnesses, and general support and loading conditions. The symmetry analysis is based on enforcing invariance of the corresponding eigenvalue problem for a group of coordinate transformations associated with buckle patterns commonly exhibited by symmetrically laminated plates. The buckle-pattern symmetries examined include a central point of inversion symmetry, one plane of reflective symmetry, and two planes of reflective symmetry.

Nemeth, Michael P.↗

NASA NTRS2012

Cubic Zig-Zag Enrichment of the Classical Kirchhoff Kinematics for Laminated and Sandwich Plates

A detailed anaylsis and examples are presented that show how to enrich the kinematics of classical Kirchhoff plate theory by appending them with a set of continuous piecewise-cubic functions. This analysis is used to obtain functions that contain the effects of laminate heterogeneity and asymmetry on the variations of the inplane displacements and transverse shearing stresses, for use with a {3, 0} plate theory in which these distributions are specified apriori. The functions used for the enrichment are based on the improved zig-zag plate theory presented recently by Tessler, Di Scuva, and Gherlone. With the approach presented herein, the inplane displacements are represented by a set of continuous piecewise-cubic functions, and the transverse shearing stresses and strains are represented by a set of piecewise-quadratic functions that are discontinuous at the ply interfaces.

Nemeth, Michael P.↗

NASA NTRS2012

The Exact Solution for Linear Thermoelastic Axisymmetric Deformations of Generally Laminated Circular Cylindrical Shells

A detailed exact solution is presented for laminated-composite circular cylinders with general wall construction and that undergo axisymmetric deformations. The overall solution is formulated in a general, systematic way and is based on the solution of a single fourth-order, nonhomogeneous ordinary differential equation with constant coefficients in which the radial displacement is the dependent variable. Moreover, the effects of general anisotropy are included and positive-definiteness of the strain energy is used to define uniquely the form of the basis functions spanning the solution space of the ordinary differential equation. Loading conditions are considered that include axisymmetric edge loads, surface tractions, and temperature fields. Likewise, all possible axisymmetric boundary conditions are considered. Results are presented for five examples that demonstrate a wide range of behavior for specially orthotropic and fully anisotropic cylinders.

Nemeth, Michael P.↗

NASA NTRS2011

An In-Depth Tutorial on Constitutive Equations for Elastic Anisotropic Materials

An in-depth tutorial on the constitutive equations for elastic, anisotropic materials is presented. Basic concepts are introduced that are used to characterize materials, and notions about how anisotropic material deform are presented. Hooke s law and the Duhamel-Neuman law for isotropic materials are presented and discussed. Then, the most general form of Hooke s law for elastic anisotropic materials is presented and symmetry requirements are given. A similar presentation is also given for the generalized Duhamel-Neuman law for elastic, anisotropic materials that includes thermal effects. Transformation equations for stress and strains are presented and the most general form of the transformation equations for the constitutive matrices are given. Then, specialized transformation equations are presented for dextral rotations about the coordinate axes. Next, concepts of material symmetry are introduced and criteria for material symmetries are presented. Additionally, engineering constants of fully anisotropic, elastic materials are derived from first principles and the specialized to several cases of practical importance.

Nemeth, Michael P.↗

NASA NTRS2011

Effect of Boundary Conditions on the Axial Compression Buckling of Homogeneous Orthotropic Composite Cylinders in the Long Column Range

Buckling loads for long isotropic and laminated cylinders are calculated based on Euler, Fluegge and Donnell's equations. Results from these methods are presented using simple parameters useful for fundamental design work. Buckling loads for two types of simply supported boundary conditions are calculated using finite element methods for comparison to select cases of the closed form solution. Results indicate that relying on Donnell theory can result in an over-prediction of buckling loads by as much as 40% in isotropic materials.

Mikulas, Martin M., Jr.↗

NASA NTRS2011

A Treatise on Equivalent-Plate Stiffnesses for Stiffened Laminated-Composite Plates and Plate-Like Lattices

A survey of studies conducted since 1914 on the use of equivalent-plate stiffnesses in modeling the overall, stiffness-critical response of stiffened plates and shells is presented. Two detailed, comprehensive derivations of first-approximation equivalent-plate stiffnesses are also presented that are based on the Reissner-Mindlin-type, first-order transverse-shear deformation theory for anisotropic plates. Equivalent-plate stiffness expressions, and a corresponding symbolic manipulation computer program, are also presented for several different stiffener configurations. These expressions are very general and exhibit the full range of anisotropies permitted by the Reissner-Mindlin-type, first-order transverse-shear deformation theory for anisotropic plates. The expressions presented in the present study were also compared with available, previously published results. For the most part, the previously published results are for special cases of the general expressions presented herein and are almost in complete agreement. Analysis is also presented that extends the use of the equivalent-plate stiffness expressions to sandwich plates.

Nemeth, Michael P.↗

NASA NTRS2010

Nondimensional Parameters and Equations for Nonlinear and Bifurcation Analyses of Thin Anisotropic Quasi-Shallow Shells

A comprehensive development of nondimensional parameters and equations for nonlinear and bifurcations analyses of quasi-shallow shells, based on the Donnell-Mushtari-Vlasov theory for thin anisotropic shells, is presented. A complete set of field equations for geometrically imperfect shells is presented in terms general of lines-of-curvature coordinates. A systematic nondimensionalization of these equations is developed, several new nondimensional parameters are defined, and a comprehensive stress-function formulation is presented that includes variational principles for equilibrium and compatibility. Bifurcation analysis is applied to the nondimensional nonlinear field equations and a comprehensive set of bifurcation equations are presented. An extensive collection of tables and figures are presented that show the effects of lamina material properties and stacking sequence on the nondimensional parameters.

Nemeth, Michael P.↗

NASA NTRS2010

Approximate Pressure Distribution in an Accelerating Launch-Vehicle Fuel Tank

A detailed derivation of the equations governing the pressure in a generic liquid-fuel launch vehicle tank subjected to uniformly accelerated motion is presented. The equations obtained are then for the Space Shuttle Superlightweight Liquid-Oxygen Tank at approximately 70 seconds into flight. This generic derivation is applicable to any fuel tank in the form of a surface of revolution and should be useful in the design of future launch vehicles

Nemeth, Michael P.↗

NASA NTRS2010

Buckling Imperfection Sensitivity of Axially Compressed Orthotropic Cylinders

Structural stability is a major consideration in the design of lightweight shell structures. However, the theoretical predictions of geometrically perfect structures often considerably over predict the buckling loads of inherently imperfect real structures. It is reasonably well understood how the shell geometry affects the imperfection sensitivity of axially compressed cylindrical shells; however, the effects of shell anisotropy on the imperfection sensitivity is less well understood. In the present paper, the development of an analytical model for assessing the imperfection sensitivity of axially compressed orthotropic cylinders is discussed. Results from the analytical model for four shell designs are compared with those from a general-purpose finite-element code, and good qualitative agreement is found. Reasons for discrepancies are discussed, and potential design implications of this line of research are discussed.

Schultz, Marc R.↗

NASA NTRS2009

Simple Formulas and Results for Buckling-Resistance and Stiffness Design of Compression-Loaded Laminated-Composite Cylinders

Simple formulas for the buckling stress of homogeneous, specially orthotropic, laminated-composite cylinders are presented. The formulas are obtained by using nondimensional parameters and equations that facilitate general validation, and are validated against the exact solution for a wide range of cylinder geometries and laminate constructions. Results are presented that establish the ranges of the nondimensional parameters and coefficients used. General results, given in terms of the nondimensional parameters, are presented that encompass a wide range of geometries and laminate constructions. These general results also illustrate a wide spectrum of behavioral trends. Design-oriented results are also presented that provide a simple, clear indication of laminate composition on critical stress, critical strain, and axial stiffness. An example is provided to demonstrate the application of these results to thin-walled column designs.

Nemeth, Michael P.↗

NASA NTRS2008

Improved Design Formulae for Buckling of Orthotropic Plates under Combined Loading

Simple, accurate buckling interaction formulae are presented for long orthotropic plates with either simply supported or clamped longitudinal edges and under combined loading that are suitable for design studies. The loads include 1) combined uniaxial compression (or tension) and shear, 2) combined pure inplane bending and 3) shear and combined uniaxial compression (or tension) and pure inplane bending. The interaction formulae are the results of detailed regression analysis of buckling data obtained from a very accurate Rayleigh-Ritz method.

Weaver, Paul M.↗

NASA NTRS2007

Bounds on Flexural Properties and Buckling Response for Symmetrically Laminated Plates

Nondimensional parameters and equations governing the buckling behavior of rectangular symmetrically laminated plates are presented that can be used to represent the buckling resistance, for plates made of all known structural materials, in a very general, insightful, and encompassing manner. In addition, these parameters can be used to assess the degree of plate orthotropy, to assess the importance of anisotropy that couples bending and twisting deformations, and to characterize quasi-isotropic laminates quantitatively. Bounds for these nondimensional parameters are also presented that are based on thermodynamics and practical laminate construction considerations. These bounds provides insight into potential gains in buckling resistance through laminate tailoring and composite-material development. As an illustration of this point, upper bounds on the buckling resistance of long rectangular orthotropic plates with simply supported or clamped edges and subjected to uniform axial compression, uniform shear, or pure inplane bending loads are presented. The results indicate that the maximum gain in buckling resistance for tailored orthotropic laminates, with respect to the corresponding isotropic plate, is in the range of 26-36% for plates with simply supported edges, irrespective of the loading conditions. For the plates with clamped edges, the corresponding gains in buckling resistance are in the range of 9-12% for plates subjected to compression or pure inplane bending loads and potentially up to 30% for plates subjected to shear loads.

Weaver, Paul M.↗

NASA NTRS2006

Collected Papers in Structural Mechanics Honoring Dr. James H. Starnes, Jr.

This special publication contains a collection of structural mechanics papers honoring Dr. James H. Starnes, Jr. presented at the 46th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference held in Austin, Texas, April 18-21, 2005. Contributors to this publication represent a small number of those influenced by Dr. Starnes' technical leadership, his technical prowess and diversity, and his technical breath and depth in engineering mechanics. These papers cover some of the research areas Dr. Starnes investigated, which included buckling, postbuckling, and collapse of structures; composite structural mechanics, residual strength and damage tolerance of metallic and composite structures; and aircraft structural design, certification and verification. He actively pursued technical understanding and clarity, championed technical excellence, and modeled humility and perseverance.

Knight, Norman F., Jr.↗

NASA NTRS2006

Application of Video Image Correlation Techniques to the Space Shuttle External Tank Foam Materials

Results that illustrate the use of a video-image-correlation-based displacement and strain measurement system to assess the effects of material nonuniformities on the behavior of the sprayed-on foam insulation (SOFI) used for the thermal protection system on the Space Shuttle External Tank are presented. Standard structural verification specimens for the SOFI material with and without cracks and subjected to mechanical or thermal loading conditions were tested. Measured full-field displacements and strains are presented for selected loading conditions to illustrate the behavior of the foam and the viability of the measurement technology. The results indicate that significant strain localization can occur in the foam because of material nonuniformities. In particular, elongated cells in the foam can interact with other geometric or material discontinuities in the foam and develop large-magnitude localized strain concentrations that likely initiate failures. Furthermore, some of the results suggest that continuum mechanics and linear elastic fracture mechanics might not adequately represent the physical behavior of the foam, and failure predictions based on homogeneous linear material models are likely to be inadequate.

Hilburger, Mark W.↗