WEINGARTEN'S CHARACTERISTIC FUNCTION AS A MEMBRANE STRESS FUNCTION
Weingartens characteristic function as a membrane stress function
STRESS↗
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The structure of Airy's stress function in multiply connected regions
In solving two-dimensional problems using Airy's stress function for multiply connected regions, the form of the function depends on the dislocations and boundary forces present. The structure of Airy's function is shown to consist of a part expressible in terms of boundary forces and a part expressible in the manner of Poincare. Meanings of the constants occurring in Poincare's expression are discussed.
FRAMES, GRIDWORKS AND TRUSSES↗
Determination of stresses in elastic solids using three stress functions and three equations
Classical equations of elasticity in terms of stress components reduced to three stress functions and three equations
Reed, R. E., Jr.↗
Approximate relations for laminar heat-transfer and shear-stress functions in equilibrium dissociated air
Approximate equations for computing enthalpy and velocity derivatives at surface of flat plate, cone, or blunt axisymmetric body
Zoby, E. V.↗
Boundary-integral methods in elasticity and plasticity
Recently developed methods that use boundary-integral equations applied to elastic and elastoplastic boundary value problems are reviewed. Direct, indirect, and semidirect methods using potential functions, stress functions, and displacement functions are described. Examples of the use of these methods for torsion problems, plane problems, and three-dimensional problems are given. It is concluded that the boundary-integral methods represent a powerful tool for the solution of elastic and elastoplastic problems.
Mendelson, A.↗
Adding stress plot function to NASTRAN
Stress plot function was developed and added to the NASTRAN level 15.5. Computed stress distribution can be displayed by this function, with vectors showing the principal stresses of the finite elements over the specified portions of the structure. NASTRAN is reviewed in the aspect of plotting capabilities. Stress tensor field is examined in preparation of stress display. Then the stress plot function as added to the NASTRAN is described. A sample plotout by this function is shown.
Katoh, S.↗
Element Library for Three-Dimensional Stress Analysis by the Integrated Force Method
The Integrated Force Method, a recently developed method for analyzing structures, is extended in this paper to three-dimensional structural analysis. First, a general formulation is developed to generate the stress interpolation matrix in terms of complete polynomials of the required order. The formulation is based on definitions of the stress tensor components in term of stress functions. The stress functions are written as complete polynomials and substituted into expressions for stress components. Then elimination of the dependent coefficients leaves the stress components expressed as complete polynomials whose coefficients are defined as generalized independent forces. Such derived components of the stress tensor identically satisfy homogenous Navier equations of equilibrium. The resulting element matrices are invariant with respect to coordinate transformation and are free of spurious zero-energy modes. The formulation provides a rational way to calculate the exact number of independent forces necessary to arrive at an approximation of the required order for complete polynomials. The influence of reducing the number of independent forces on the accuracy of the response is also analyzed. The stress fields derived are used to develop a comprehensive finite element library for three-dimensional structural analysis by the Integrated Force Method. Both tetrahedral- and hexahedral-shaped elements capable of modeling arbitrary geometric configurations are developed. A number of examples with known analytical solutions are solved by using the developments presented herein. The results are in good agreement with the analytical solutions. The responses obtained with the Integrated Force Method are also compared with those generated by the standard displacement method. In most cases, the performance of the Integrated Force Method is better overall.
Kaljevic, Igor↗
Morphological and functional manifestations of rat adrenal-cortex response to sodium bromide administration under hypodynamic stress
Functional and morphological manifestations of adrenal cortex response to hypodynamia (2-hr immobilization on an operating table) under the influence of bromine preparations were studied. The sodium bromide was administered intraperitoneally in 100, 250, and 500 mg/kg doses once and repeatedly during ten days. The adrenal gland was evaluated functionally by ascorbic acid and cholesterol content and morphologically by coloring it with hematoxylin-eosin and Sudans for lipid revealing at freezing. Results are displayed in two tables and microphotographs. They are summarized as follows: the bromine weakens the functional state of the adrenal cortex in intact rats, causing changes similar to those under stress. During immobilization combined with preliminary bromine administration, a less pronounced stress reaction is noticeable.
Kirichek, L. T.↗
Accurate Thermal Stresses for Beams: Normal Stress
Formulations for a general theory of thermoelasticity to generate accurate thermal stresses for structural members of aeronautical vehicles were developed in 1954 by Boley. The formulation also provides three normal stresses and a shear stress along the entire length of the beam. The Poisson effect of the lateral and transverse normal stresses on a thermally loaded beam is taken into account in this theory by employing an Airy stress function. The Airy stress function enables the reduction of the three-dimensional thermal stress problem to a two-dimensional one. Numerical results from the general theory of thermoelasticity are compared to those obtained from strength of materials. It is concluded that the theory of thermoelasticity for prismatic beams proposed in this paper can be used instead of strength of materials when precise stress results are desired.
Johnson, Theodore F.↗
Accurate Thermal Stresses for Beams: Normal Stress
Formulations for a general theory of thermoelasticity to generate accurate thermal stresses for structural members of aeronautical vehicles were developed in 1954 by Boley. The formulation also provides three normal stresses and a shear stress along the entire length of the beam. The Poisson effect of the lateral and transverse normal stresses on a thermally loaded beam is taken into account in this theory by employing an Airy stress function. The Airy stress function enables the reduction of the three-dimensional thermal stress problem to a two-dimensional one. Numerical results from the general theory of thermoelasticity are compared to those obtained from strength of materials. It is concluded that the theory of thermoelasticity for prismatic beams proposed in this paper can be used instead of strength of materials when precise stress results are desired.
Johnson, Theodore F.↗
Regulation of the Adrenal Cortex Function During Stress
A proposal to study the function of the adrenal gland in the rat during stress is presented. In the proposed project, three different phases of experimentation will be undertaken. The first phase includes establishment of the circadian rhythm of both brain amines and glucocoticoids, under normal conditions and under chronic and acute stressful conditions. The second phase includes the study of the pharmacokinetics of glucocorticoid binding under normal and stress conditions. The third phase includes brain uptake and binding under different experimental conditions. In the outlined experiments brain biogenic amines will be evaluated, adrenal functions will be measured and stress effect on those parameters will be studied. It is hoped that this investigation can explain some of the complex relationships between the brain neurotransmitter and adrenal function.
Soliman, K. F. A.↗
Comparison of surface fluxes and conductances at two contrasting sites within the FIFE area
Surface flux measurements from two contrasting sites within the FIFE study area are analyzed. The seasonal variation of midday latent heat fluxes and surface conductances at the two sites was found to be very similar even though the ratio of their average total leaf area indices was greater than two to one. Concurrent measurements made at another six flat sites within the FIFE area confirmed the independence of latent heat flux with respect to leaf area index. The surface conductance stress function related to specific humidity deficit was the same for the two sites, whereas the solar radiation stress function showed a difference of 30 percent at a solar radiation input of 300 W/sq m and the soil moisture stress function showed a difference of 16 percent when half the extractable soil moisture had been taken up. However, when the stress functions were combined to determine the surface conductance, these differences virtually canceled out.
Stewart, J. B.↗
Completed Beltrami-Michell Formulation for Analyzing Radially Symmetrical Bodies
A force method formulation, the completed Beltrami-Michell formulation (CBMF), has been developed for analyzing boundary value problems in elastic continua. The CBMF is obtained by augmenting the classical Beltrami-Michell formulation with novel boundary compatibility conditions. It can analyze general elastic continua with stress, displacement, or mixed boundary conditions. The CBMF alleviates the limitations of the classical formulation, which can solve stress boundary value problems only. In this report, the CBMF is specialized for plates and shells. All equations of the CBMF, including the boundary compatibility conditions, are derived from the variational formulation of the integrated force method (IFM). These equations are defined only in terms of stresses. Their solution for kinematically stable elastic continua provides stress fields without any reference to displacements. In addition, a stress function formulation for plates and shells is developed by augmenting the classical Airy's formulation with boundary compatibility conditions expressed in terms of the stress function. The versatility of the CBMF and the augmented stress function formulation is demonstrated through analytical solutions of several mixed boundary value problems. The example problems include a composite circular plate and a composite circular cylindrical shell under the simultaneous actions of mechanical and thermal loads.
Kaljevic, Igor↗
Free-edge effects in laminates under extension, bending and twisting. II - Sublaminate/layer modeling and analysis
The stress-function-based variational method of Yin (1991) is extended and modified into a combined layer/sublaminate approach applicable to a laminated strip composed of a large number of differently orientated, anisotropic elastic plies. Lekhnitskii's (1963) stress functions are introduced into two interior layers adjacent to a particular interface. The remaining layers are grouped into an upper sublaminate and a lower sublaminate. The stress functions are expanded in truncated power series of the thickness coordinate, and the differential equations governing the coefficient functions are derived by using the complementary virtual work principle. The layer/sublaminate approach limits the dimension of the eigenvalue problem to a fixed number irrespective of the number of layers in the sublaminate, so that reasonably accurate solutions of the interlaminar stresses can be computed with extreme ease. For symmetric, four-layer, angle-ply and cross-ply laminates, a comparison of the previous analysis results based on the pure layer model and new results based on two different layer/sublaminate models indicates reasonable over-all agreement in the interlaminar stresses and superior agreement in the total peeling and shearing force.
Yin, Wan-Lee↗
On the state of membrane stress of shells of revolution with positive curvature
Integral stress function for state of membrane stress in shells of revolution formed by second- order surface
MEMBRANE FORCE↗
Analysis of the shearout failure mode in composite bolted joints
A semi-empirical shearout strength model has been formulated for the analysis of composite bolted joints with allowance for the effects of joint geometry. The model employs a polynomial stress function in conjunction with a point stress failure criterion to predict strength as a function of fastener size, edge distance, and half spacing. The stress function is obtained by two-dimensional plane-stress finite element analysis using quadrilateral elements with orthotropic material properties. Comparison of experimentally determined shearout strength data with model predicted failures has substantiated the accuracy of the model.
Wilson, D. W.↗
The relationship between the microwave radar cross section and both wind speed and stress: Model function studies using Frontal Air-Sea Interaction Experiment data
The Frontal Air-Sea Interaction Experiment (FASINEX) provided a unique data set with coincident airborne scatterometer measurements of the ocean surface radar cross section (RCS)(at Ku band) and near-surface wind and wind stress. These data have been analyzed to study new model functions which relate wind speed and surface friction velocity (square root of the kinematic wind stress) to the radar cross section and to better understand the processes in the boundary layer that have a strong influence on the radar backscatter. Studies of data from FASINEX indicate that the RCS has a different relation to the friction velocity than to the wind speed. The difference between the RCS models using these two variables depends on the polarization and the incidence angle. The radar data have been acquired from the Jet Propulsion Laboratory airborne scatterometer. These data span 10 different flight days. Stress measurements were inferred from shipboard instruments and from aircraft flying at low altitudes, closely following the scatterometer. Wide ranges of radar incidence angles and environmental conditions needed to fully develop algorithms are available from this experiment.
Weissman, David E.↗
Stress Formulation in Three-Dimensional Elasticity
The theory of elasticity evolved over centuries through the contributions of eminent scientists like Cauchy, Navier, Hooke Saint Venant, and others. It was deemed complete when Saint Venant provided the strain formulation in 1860. However, unlike Cauchy, who addressed equilibrium in the field and on the boundary, the strain formulation was confined only to the field. Saint Venant overlooked the compatibility on the boundary. Because of this deficiency, a direct stress formulation could not be developed. Stress with traditional methods must be recovered by backcalculation: differentiating either the displacement or the stress function. We have addressed the compatibility on the boundary. Augmentation of these conditions has completed the stress formulation in elasticity, opening up a way for a direct determination of stress without the intermediate step of calculating the displacement or the stress function. This Completed Beltrami-Michell Formulation (CBMF) can be specialized to derive the traditional methods, but the reverse is not possible. Elasticity solutions must be verified for the compliance of the new equation because the boundary compatibility conditions expressed in terms of displacement are not trivially satisfied. This paper presents the variational derivation of the stress formulation, illustrates the method, examines attributes and benefits, and outlines the future course of research.
Patnaik, Surya N.↗