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At least 181 records · Page 10

A multilevel approach for minimum weight structural design including local and system buckling constraints

A rational multilevel approach for minimum weight structural design of truss and wing structures including local and system buckling constraints is presented. Overall proportioning of the structure is achieved at the system level subject to strength, displacement and system buckling constraints, while the detailed component designs are carried out separately at the component level satisfying local buckling constraints. Total structural weight is taken to be the objective function at the system level while employing the change in the equivalent system stiffness of the component as the component level objective function. Finite element analysis is used to predict static response while system buckling behavior is handled by incorporating a geometric stiffness matrix capability. Buckling load factors and the corresponding mode shapes are obtained by solving the eigenvalue problem associated with the assembled elastic stiffness and geometric stiffness matrices for the structural system. At the component level various local buckling failure modes are guarded against using semi-empirical formulas. Mathematical programming techniques are employed at both the system and component level.

Schmit, L. A., Jr.↗

Large-deflection theory for end compression of long rectangular plates rigidly clamped along two edges

The von Karman equations for flat plates are solved beyond the buckling load up to edge strains equal to eight time the buckling strain, for the extreme case of rigid clamping along the edges parallel to the load. Deflections, bending stresses, and membrane stresses are given as a function of end compressive load. The theoretical values of effective width are compared with the values derived for simple support along the edges parallel to the load. The increases in effective width due to rigid clamping drops from about 20 percent near the buckling strain to about 8 percent at an edge strain equal to eight times the buckling strain. Experimental values of effective width in the elastic range reported in NACA Technical Note No. 684 are between the theoretical curves for the extremes of simple support and rigid clamping.

Levy, Samuel↗

Advances and trends in plate buckling research

Advances and current trends in plate bucklin research are summarized. The field is divided into three parts: (1) classical buckling studies, including plates of rectangular, circular and other shapes; (2) classical complicating effects, including elastic foundation, anisotropic material, variable thickness, shear deformation and nonhomogeneous material; and (3) nonclassical considerations, including postbuckling, imperfections, parametric excitation, follower forces, magnetoelastic buckling and inelastic buckling.

Leissa, A.↗

Critical Compressive Stress for Flat Rectangular Plates Supported Along All Edges and Elastically Restrained Against Rotation along the Unloaded Edges

A chart is presented for the values of the coefficient in the formula for the critical compressive stress at which buckling may be expected to occur in flat rectangular plates supported along all edges and, in addition, elastically restrained against rotation along the unloaded edges. The mathematical derivations of the formulas required in the construction of the chart are given.

Lundquist, Eugene E↗

Critical Compressive Stress for Flat Rectangular Plates Supported Along all Edges and Elastically Restrained Against Rotation Along the Unloaded Edges, Special Report 189

A chart is presented for the values of the coefficient in the formula for the critical compressive stress at which buckling may be expected to occur in flat rectangular plates supported along all edges and, in addition, elastically restrained against rotation along the unloaded edges. The mathematical derivations of the formulas required in the construction of the chart are given.

Lundquist, Eugene E.↗

Design, Optimization, and Evaluation of Integrally-Stiffened Al-2139 Panel with Curved Stiffeners

A curvilinear stiffened panel was designed, manufactured, and tested in the Combined Load Test Fixture at NASA Langley Research Center. The panel is representative of a large wing engine pylon rib and was optimized for minimum mass subjected to three combined load cases. The optimization included constraints on web buckling, material yielding, crippling or local stiffener failure, and damage tolerance using a new analysis tool named EBF3PanelOpt. Testing was performed for the critical combined compression-shear loading configuration. The panel was loaded beyond initial buckling, and strains and out-of-plane displacements were extracted from a total of 20 strain gages and 6 linear variable displacement transducers. The VIC-3D system was utilized to obtain full field displacements/strains in the stiffened side of the panel. The experimental data were compared with the strains and out-of-plane deflections from a high fidelity nonlinear finite element analysis. The experimental data were also compared with linear elastic finite element results of the panel/test-fixture assembly. Overall, the panel buckled very near to the predicted load in the web regions.

Havens, David↗

Cell prestress. II. Contribution of microtubules

The tensegrity model hypothesizes that cytoskeleton-based microtubules (MTs) carry compression as they balance a portion of cell contractile stress. To test this hypothesis, we used traction force microscopy to measure traction at the interface of adhering human airway smooth muscle cells and a flexible polyacrylamide gel substrate. The prediction is that if MTs balance a portion of contractile stress, then, upon their disruption, the portion of stress balanced by MTs would shift to the substrate, thereby causing an increase in traction. Measurements were done first in maximally activated cells (10 microM histamine) and then again after MTs had been disrupted (1 microM colchicine). We found that after disruption of MTs, traction increased on average by approximately 13%. Because in activated cells colchicine induced neither an increase in intracellular Ca(2+) nor an increase in myosin light chain phosphorylation as shown previously, we concluded that the observed increase in traction was a result of load shift from MTs to the substrate. In addition, energy stored in the flexible substrate was calculated as work done by traction on the deformation of the substrate. This result was then utilized in an energetic analysis. We assumed that cytoskeleton-based MTs are slender elastic rods supported laterally by intermediate filaments and that MTs buckle as the cell contracts. Using the post-buckling equilibrium theory of Euler struts, we found that energy stored during buckling of MTs was quantitatively consistent with the measured increase in substrate energy after disruption of MTs. This is further evidence supporting the idea that MTs are intracellular compression-bearing elements.

Non-NASA Center↗

Buckling Of Long Compression-Loaded Anisotropic Plates Restrained Against Inplane Lateral and Shear Deformations

An approach for synthesizing buckling results and behavior for thin balanced and unbalanced symmetric laminates that are subjected to uniform axial compression loads and elastically restrained against inplane expansion, contraction, and shear deformation is presented. This approach uses a nondimensional analysis for infinitely long, flexurally anisotropic plates (coupling between bending and twisting) that are subjected to combined mechanical loads and is based on nondimensional parameters. In addition, nondimensional loading parameters are derived that account for the effects of the elastic inplane deformation restraints, membrane orthotropy, and membrane anisotropy on the induced prebuckling stress state. The loading parameters are used to determine buckling coefficients that include the effects of flexural orthotropy and flexural anisotropy. Many results are presented, for some selected laminates, that are intended to facilitate a structural designer's transition to the use of the generic buckling design curves that are presented and discussed in the paper. Several buckling response curves are presented that provide physical insight into the behavior for combined loads, in addition to providing useful design data. An example is presented that demonstrates the use of the generic design curves, which are applicable to a wide range of laminate constructions. The analysis approach and generic results indicate the effects and characteristics of laminate orthotropy and anisotropy in a very general and unifying manner.

Nemeth, Michael P.↗

Buckling of continuously supported hinged beams

The effect on the buckling load of a hinge at the center of an infinite beam supported by a semiinfinite elastic continuum is analyzed using the complex Fourier transforms. An expression is obtained for the relationship between the surface deflection of the elastic continuum and the pressure distribution acting on the surface, and solutions are obtained for the assumed form of the pressure distribution below the beam. The analysis is applied to cases of uniform pressure over the width of the beam and a pressure distribution that occurs below a rigid stamp. The results show that the buckling loads for an infinite beam with a hinge at the center and supported by a semiinfinite elastic continuum are approximately one half of those for a beam without a hinge, and that this ratio is exactly one half for an infinite beam resting on a Winkler foundation.

Murthy, G. K. N.↗

Stability, vibration and passive damping of partially restrained imperfect columns

A theoretical and experimental study of slender tubular columns for possible use in space structures is conducted in the presence of partial rotational end restraints. Explicit formulas are derived for computing the buckling load and the lowest natural frequency of perfectly straight uniform elastic members with rotational end restraints possessing linear moment-rotation characteristics. An exact solution in the form of a transcendental equation, and a numerical solution using second-order finite-differences are also presented. The presence of an initial imperfection is also incorporated into the numerical procedure. Vibration tests are conducted on an imperfect tubular steel member in the absence of an axial load. A damping concept consisting of a string-mass assembly is explored. Three passive damping configurations involving combinations of three lead shots were investigated. The three lead shot configurations provided considerably greater damping than the single lead shot.

Razzaq, Z.↗

A Simplified Method of Elastic-Stability Analysis for Thin Cylindrical Shells

This paper develops a new method for determining the buckling stresses of cylindrical shells under various loading conditions. In part I, the equation for the equilibrium of cylindrical shells introduced by Donnell in NACA report no. 479 to find the critical stresses of cylinders in torsion is applied to find critical stresses for cylinders with simply supported edges under other loading conditions. In part II, a modified form of Donnell's equation for the equilibrium of thin cylindrical shells is derived which is equivalent to Donnell's equation but has certain advantages in physical interpretation and in ease of solution, particularly in the case of shells having clamped edges. The question of implicit boundary conditions is also considered.

Batdorf, S B↗

An integrated approach to the synthesis of geometrically non-linear structures

An integrated approach to the minimum weight design of geometrically nonlinear three-dimensional truss structures with geometric imperfections, subject to inequality constraints on static displacements, stresses, local buckling and cross sectional areas, is investigated. The integrated structural synthesis problem involves design and response quantities as independent variables and equilibrium equations, describing the finite element model, as equality constraints. The nonlinear structural analysis and the optimization are thus merged together into a single process. A computer program developed to compute the constraint values and analytical gradients is coupled with a generalized reduced gradient algorithm to solve the integrated problem. Numerical results for a geometrically nonlinear shallow dome example problem are presented for various types of imperfections. Furthermore, it is found that the algorithm is capable of detecting and guarding against system as well as element elastic instability using equilibrium information only, that is, without imposing system and local buckling inequality constraints.

Smaoui, H.↗

Scalability in SLA lattice through lattice orientation and hybrid frame and plate architectures

Lightweighting has been a key goal for engineers and designers, with lattice structures widely explored as the building blocks for structural components. Cellular structure-inspired lattice truss frame designs made of struts, have been extensively studied. All plate-based lattice designs have superior mechanical performance. Limits in scalability occur from formation of closed pockets limiting uv curing in processes like stereolithography (SLA). We examine hybrid frame and plate body-centered cubic-simply cubic (BCC-SC) lattices under compression. Unit cells and scaled up lattice exhibit an increase in yield stress and modulus with the addition of plates. The loading direction on the hybrid frame and plate unit cells affected the magnitude of improvement. Simulations and measurements indicated that the optimal lightweight lattice was determined to be when two plates were placed opposite each other with plates buttressing the struts, inhibiting buckling of the struts aligned with the loading direction. This lattice resulted in 63% improvement in specific modulus, a 137% improvement in specific yield point, and a 360% improvement in specific energy absorption (SEA) and the scaled up 4 × 4 × 4 scaled-up structures, showed a 107%, 148%, and 297% in specific modulus, specific yield point, and SEA, respectively A combined stretching-bending behavior was identified in optimal orientations reflecting the delayed buckling mechanism paired to a rising stress-strain curve past the elastic yield indicating bending resistance. The mass moment of inertia was found to be a key parameter correlating optimum orientation for the same number of plates added to the BCC-SC frame.

Mahan Ghosh↗

A small-deflection theory for curved sandwich plates

A small-deflection theory that takes into account deformations due to transverse shear is presented for the elastic-behavior analysis of orthotropic plates of constant cylindrical curvature, with consideration of buckling included. The theory is applicable primarily to sandwich construction. (author)

Stein, Manuel↗

BUCLAP2: A computer program for instability analysis of laminated long plates subjected to combined inplane loads

This program description document describes the program structure and the design details of a CDC 6600 FORTRAN 4 digital computer program, BUCLAP2, which uses minimum energy principles to do an elastic stability analysis of curved and flat laminated rectangular long plates subjected to combined inplane normal and shear loads. Given the geometry, the material properties, and slected boundary conditions for the plate element, the program calculates the minimum buckling load for various wave lengths. The two parallel ends of the program calculates the minimum buckling load for various wave lengths. The two parallel ends of the long plate must be simply supported and arbitrary elastic boundary conditions may be imposed along either one or both external longitudinal sides. For guide to program use, see

Halstead, D. W.↗