The strongest column - An energy approach.
Column shape for maximum Euler buckling load determined using energy method calculations
EULER BUCKLING↗
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Energy considerations in the analysis of stability of nonconservative structural systems.
Energy method extended to stability analysis of linear system under action of nonconservative forces
FLUTTER ANALYSIS↗
Structural analysis of an NDE-inspected carbon-carbon component
In this research, it is demonstrated that the integration of nondestructive evaluation with the finite element method (a quantitative NDE/FEM approach) can be used for analysis and behavior prediction of advanced materials, such as fiber composites, after processing and during in-service testing. First, stress, strain, and energy data were calculated by the finite element method for square plates with a 10 percent difference in the material properties between specified segments, i.e., between the center and the outside section or between two halves of the plate. This demonstrated the efficiency of the method in predicting variations in the structural behavior based on small material property differences. Then, finite element analyses and actual axial compression tests were performed on a Space Shuttle brake stator made from woven carbon-carbon composites. The material properties used in the numerical modeling of the stator were previously characterized at a large number of points on the component by quantitative NDE-procedures, i.e., ultrasonics and radiography. The results from the experimental compressive loading tests were used to verify the NDE/FEM results. Good agreement was found for most parameters.
Striz, A. G.↗
Compatible thermal and structural elements for the analysis of beam and plate structures
Energy methods are used to formulate steady-state thermal elements which are compatible with structural beam and plate elements. Comparisons of energy method results with finite element results indicate that the energy methods achieve similar accuracy with fewer degrees of freedom. Limitations of energy methods with regard to discontinuous functions and computational overflow are noted. Thermal stress calculations are simplified by the use of similar formulations for the thermal and structural elements. The advantages that these energy-based elements offer to high-temperature structural optimization are discussed.
Vause, R. F.↗
Comparison of full 3-D, thin-film 3-D, and thin-film plate analyses of a postbuckled embedded delamination
Local buckling can cause large interlaminar stresses along the delamination front, which can lead to delamination growth. This paper examines several methods of calculating strain-energy release rates, which are often used to predict delamination growth. The thin-film plate analysis, which was least expensive, calculated the total strain-energy release rate G(T) quite accurately. However, the stress field along the delamination front is highly mixed-mode and has no fixed ratio of G(I) to G(II). Since plate analysis can only calculate G(T), it would not be useful for accurate predictions of delamination growth if mode mix is important.
Whitcomb, John D.↗
Development of Finite Elements for Two-Dimensional Structural Analysis Using the Integrated Force Method
The Integrated Force Method has been developed in recent years for the analysis of structural mechanics problems. This method treats all independent internal forces as unknown variables that can be calculated by simultaneously imposing equations of equilibrium and compatibility conditions. In this paper a finite element library for analyzing two-dimensional problems by the Integrated Force Method is presented. Triangular- and quadrilateral-shaped elements capable of modeling arbitrary domain configurations are presented. The element equilibrium and flexibility matrices are derived by discretizing the expressions for potential and complementary energies, respectively. The displacement and stress fields within the finite elements are independently approximated. The displacement field is interpolated as it is in the standard displacement method, and the stress field is approximated by using complete polynomials of the correct order. A procedure that uses the definitions of stress components in terms of an Airy stress function is developed to derive the stress interpolation polynomials. Such derived stress fields identically satisfy the equations of equilibrium. Moreover, the resulting element matrices are insensitive to the orientation of local coordinate systems. A method is devised to calculate the number of rigid body modes, and the present elements are shown to be free of spurious zero-energy modes. A number of example problems are solved by using the present library, and the results are compared with corresponding analytical solutions and with results from the standard displacement finite element method. The Integrated Force Method not only gives results that agree well with analytical and displacement method results but also outperforms the displacement method in stress calculations.
Kaljevic, Igor↗
Behavior of a Cantilever Plate Under Rapid-heating Conditions
The temperature distributions encountered in thin solid wings subjected to aerodynamic heating induce thermal stresses that may effectively reduce the stiffness of the wing. The effects of this reduction in stiffness were investigated experimentally by rapidly heating the edges of a cantilever plate. The midplane thermal stresses imposed by the nonuniform temperature distribution caused the plate to buckle torsionally, increased the deformations of the plate under a constant applied torque, and reduced the frequency of the first two natural modes of vibration. By using small-deflection theory and employing energy methods, the effect of nonuniform heating on the plate stiffness was calculated. The theory predicts the general effects of the thermal stresses, but becomes inadequate as the temperature difference increases and plate deflections become large.
Vosteen, Louis F↗
Local instability of columns with I-, Z-, channel, and rectangular-tube sections
Charts are presented for the coefficients in the formulas for the critical compressive stress at which cross-sectional distortion begins in thin-wall columns of I-, Z-, channel, and rectangular-tube sections. The energy method of Timoshenko was used in the theoretical calculations required for the construction of the charts. The deflection equations were carefully selected to give good accuracy. The calculation of the critical compressive stress at stresses above the elastic range is briefly discussed in order to demonstrate the use of the formulas and the charts in engineering calculations. Two illustrative problems are included.
STRESSED SKIN LMAL↗
Monitoring Loads In Fiber-Reinforced Composite Materials
In new method of determining load on specimen, direction of stress wave propagation measured by array of acoustic sensors attached to specimen. Responses of sensors analyzed by strain-energy-density calculations to calculate load. Change in anisotropy of elasticity caused by applied load and corresponding induced strain. Is means to monitor applied load corresponding to measurable shift in direction of propagation of stress wave. Monitoring device based on this method made integral part of airframe in which unidirectional section of structure, such as spar cap or longeron, carries primary load.
Prosser, William H.↗
Local instability of centrally loaded columns of channel section and Z-section
Charts are presented for the coefficients in formulas for the critical compressive stress at which cross-sectional distortion begins in a thin-wall member with either a channel section or a Z-section with identical flanges. The energy method of Timoshenko was used in the theoretical calculations required for the construction of the charts. The deflection equations were carefully selected to give good accuracy. The calculation of the critical compressive stress at stresses beyond the elastic range is briefly discussed. In order to demonstrate the use of the formulas and the charts in engineering calculations, two illustrative problems are included.
ELASTICITY↗
SCARE: A post-processor program to MSC/NASTRAN for the reliability analysis of structural ceramic components
A computer program was developed for calculating the statistical fast fracture reliability and failure probability of ceramic components. The program includes the two-parameter Weibull material fracture strength distribution model, using the principle of independent action for polyaxial stress states and Batdorf's shear-sensitive as well as shear-insensitive crack theories, all for volume distributed flaws in macroscopically isotropic solids. Both penny-shaped cracks and Griffith cracks are included in the Batdorf shear-sensitive crack response calculations, using Griffith's maximum tensile stress or critical coplanar strain energy release rate criteria to predict mixed mode fracture. Weibull material parameters can also be calculated from modulus of rupture bar tests, using the least squares method with known specimen geometry and fracture data. The reliability prediction analysis uses MSC/NASTRAN stress, temperature and volume output, obtained from the use of three-dimensional, quadratic, isoparametric, or axisymmetric finite elements. The statistical fast fracture theories employed, along with selected input and output formats and options, are summarized. An example problem to demonstrate various features of the program is included.
Gyekenyesi, J. P.↗
SCARE - A postprocessor program to MSC/NASTRAN for reliability analysis of structural ceramic components
A computer program was developed for calculating the statistical fast fracture reliability and failure probability of ceramic components. The program includes the two-parameter Weibull material fracture strength distribution model, using the principle of independent action for polyaxial stress states and Batdorf's shear-sensitive as well as shear-insensitive crack theories, all for volume distributed flaws in macroscopically isotropic solids. Both penny-shaped cracks and Griffith cracks are included in the Batdorf shear-sensitive crack response calculations, using Griffith's maximum tensile stress or critical coplanar strain energy release rate criteria to predict mixed mode fracture. Weibull material parameters can also be calculated from modulus of rupture bar tests, using the least squares method with known specimen geometry and fracture data. The reliability prediction analysis uses MSC/NASTRAN stress, temperature and volume output, obtained from the use of three-dimensional, quadratic, isoparametric, or axisymmetric finite elements. The statistical fast fracture theories employed, along with selected input and output formats and options, are summarized. An example problem to demonstrate various features of the program is included.
Gyekenyesi, J. P.↗
Unsteady turbulent boundary layers in two-dimensional, incompressible flow.
The paper presents the results of some calculations aimed at studying the characteristics of turbulent boundary layers in unsteady flow. The calculations were performed using the method of Singleton and Nash, which is based on the turbulent kinetic energy equation. Emphasis is placed on the approach to zero wall stress, and the results show the extent to which onset of this condition can be delayed by the effects of time dependence. The delay is not associated merely with alleviation of the pressure gradients, and quasi-steady methods cannot readily be used to calculate this type of flow.
Nash, J. F.↗
Local instability of symmetrical rectangular tubes under axial compression
A chart is presented for the coefficient in the formula for the critical compressive stress at which cross sectional distortion begins in a thin-wall tube of rectangular section symmetrical about its two principal axes. The energy method of Timoshenko was used in the theoretical calculations required for the construction of the chart. The deflection equation used in this method was selected to give good accuracy. The exact values given by solution of the differential equation were calculated for a number of cases and it was found that the energy solution was correct to within a fraction of 1 percent. The calculation of the critical compressive stress at stresses above the elastic range is also discussed. In order to demonstrate the use of the formulas and the chart in engineering calculations, several illustrative problems are included.
TUBING, RECTANGULAR - STRESSES, COMPRESSIVE↗
Impact tensile testing of wires
The test consists of fixing one end of a wire specimen and allowing a threaded falling weight to strike the other. Assuming the dynamic stress in the wire to be a function only of its strain, energy considerations show for negligible wire inertia effects that the governing dynamic stress-strain law can be determined directly from impact energy vs. wire elongation data. Theoretical calculations are presented which show negligible wire inertia effects for ratios of wire mass to striking mass of the order of .01 or less. The test method is applied to soft copper wires and the dynamic stress-strain curve so determined is found to be about 30 percent higher than the corresponding static curve.
Dawson, T. H.↗
Strain-energy-release rate analysis of the end-notched flexure specimen using the finite-element method
Two-dimensional finite-element analysis of the end-notched flexure specimen was performed using 8-node isoparametric, parabolic elements to evaluate compliance and mode II strain energy release rates, G sub II. The G sub II values were computed using two different techniques: the virtural crack-closure technique (VCCT) and the rate of change of compliance with crack length (compliance derivative method). The analysis was performed for various crack-length-to-semi-span (a/L) ratios ranging from 0.2 to 0.9. Three material systems representing a wide range of material properties were analyzed. The compliance and strain energy release rates of the specimen calculated with the present finite-element analysis agree very well with beam theory equations including transverse shear. The G sub II values calculated using the compliance derivative method compared extremely well with those calculated using the VCCT. The G sub II values obtained by the compliance derivative method using the top or bottom beam deflections agreed closely with each other. The strain energy release rates from a plane-stress analysis were higher than the plane-strain values by only a small percentage, indicating that either assumption may be used in the analysis. The G sub II values for one material system calculated from the finite-element analysis agreed with one solution in the literature and disagreed with the other solution in the literature.
Salpekar, S. A.↗
Strain energy release rate analysis of the end-notched flexure specimen using the finite-element method
Two-dimensional finite-element analysis of the end-notched flexure specimen was performed using 8-node isoparametric, parabolic elements to evaluate compliance and mode II strain energy release rates, G sub II. The G sub II values were computed using two different techniques: the virtual crack-closure technique (VCCT) and the rate of change of compliance with crack length (compliance derivative method). The analysis was performed for various crack-length-to-semi-span (a/L) ratios ranging from 0.2 to 0.9. Three material systems representing a wide range of material properties were analyzed. The compliance and strain energy release rates of the specimen calculated with the present finite-element analysis agree very well with beam theory equations including transverse shear. The G sub II values calculated using the compliance derivative method compared extremely well with those calculated using the VCCT. The G sub II values obtained by the compliance derivative method using the top or bottom beam deflections agreed closely with each other. The strain energy release rates from a plane-stress analysis were higher than the plane-strain values by only a small percentage, indicating that either assumption may be used in the analysis. The G sub II values for one material system calculated from the finte-element analysis agreed with one solution in the literature and disagreed with the other solution in the literature.
Salpekar, S. A.↗
Analysis of progressive damage in thin circular laminates due to static-equivalent impact loads
Clamped circular graphite/epoxy plates (25.4, 38.1, and 50.8 mm radii) with an 8-ply quasi-isotropic layup were analyzed for static-equivalent impact loads using the minimum-total-potential-energy method and the von Karman strain-displacement equations. A step-by-step incremental transverse displacement procedure was used to calculate plate load and ply stresses. The ply failure region was calculated using the Tsai-Wu criterion. The corresponding failure modes (splitting and fiber failure) were determined using the maximum stress criteria. The first-failure mode was splitting and initiated first in the bottom ply. The splitting-failure thresholds were relatively low and tended to be lower for larger plates than for small plates. The splitting-damage region in each ply was elongated in its fiber direction; the bottom ply had the largest damage region. The calculated damage region for the 25.4-mm-radius plate agreed with limited static test results from the literature.
Shivakumar, K. N.↗