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A closed form expression for the weight function for a strip with a single edge crack is presented. The expression is valid for relative crack lengths from zero to unity. It is based on the assumption that the shape of an opened edge crack can be approximated by a conic section. The results agree well with published values for weight functions, stress intensity factors, and crack mouth opening displacements.
A three-dimensional hybrid-stress finite element analysis of composite laminates containing cutouts and cracks is presented. Fully three-dimensional, hexahedral isoparametric elements of the hybrid-stress model are formulated on the basis of the Hellinger-Reissner variational principle. Traction-free edges, cutouts, and crack surfaces are modeled by imposition of exact traction boundary conditions along element surfaces. Special boundary and surface elements are constructed by introducing proper constraints on assumed stress functions. The Lagrangian multiplier technique is used to enforce ply-interface continuity conditions in hybrid bimaterial composite elements for modeling the interface region in a composite laminate. Two examples are given to illustrate the capability of the present method of approach: (1) the well-known delamination problem in an angle-ply laminate, and (2) the important problem of a composite laminate containing a circular hole. Results are presented in detail for each case. Implications of interlaminar and intralaminar crack initiation, growth and fracture in composites containing cracks and cutouts are discussed.
A numerical implementation of design sensitivity analysis of builtup structures is presented, using the versatility and convenience of an existing finite element structural analysis code and its database management system. The finite element code used in the implemenatation presented is the Engineering Analysis Language (EAL), which is based on a hybrid method of analysis. It was shown that design sensitivity computations can be carried out using the database management system of EAL, without writing a separate program and a separate database. Conventional (sizing) design parameters such as cross-sectional area of beams or thickness of plates and plane elastic solid components are considered. Compliance, displacement, and stress functionals are considered as performance criteria. The method presented is being extended to implement shape design sensitivity analysis using a domain method and a design component method.
A numerical implementation of shape design sensitivity analysis of built-up structures is presented, using the versatility and convenience of an existing finite element structural analysis code and its data base management system. This report is a continuation of a previous report on conventional design parameters. The finite element code used in the implementation presented is the Engineering Analysis Language (EAL), which is based on a hybrid analysis method. It has been shown that shape design sensitivity computations can be carried out using the database management system of EAL, without writing a separate program and a separate data base. The material derivative concept of continuum mechanics and an adjoint variable method of design sensitivity analysis are used to derive shape design sensitivity information of structural performances. A domain method of shape design sensitivity analysis and a design component method are used. Displacement and stress functionals are considered as performance criteria.
A methodology for computing the stresses at the interface between the skin and stiffener in stiffened composite panels is described. The methodology is based on finite-element analyses and on elasticity solution. The finite-element analyses are standard, while the elasticity solution is based on eigenvalue expansions of the stress function. The eigenvalue expansions are assumed to be valid in the local region where the stiffener flange terminates. The local elasticity solution is coupled to the global finite-element analysis using collocation on the boundary of the local region. Accuracy and convergence of the method are discussed and several examples of its utility are presented.
The hole-drilling technique for the measurement of residual stresses using electrical resistance strain gages has been widely used for isotropic materials and has been adopted by the ASTM as a standard method. For thin isotropic plates, with a hole drilled through the thickness, the idealized hole-drilling calibration constants are obtained by making use of the well-known Kirsch's solution. In this paper, an analogous attempt is made to theoretically determine the three idealized hole-drilling calibration constants for thin orthotropic materials by employing Savin's (1961) complex stress function approach.
The Boundary Force Method (BFM), a form of indirect boundary element method, is used to analyze composite laminates with cracks. The BFM uses the orthotropic elasticity solution for a concentrated horizontal and vertical force and a moment applied at a point in a cracked, infinite sheet as the fundamental solution. The necessary stress functions for this fundamental solution were formulated using the complex variable theory of orthotropic elasticity. The current method is an improvement over a previous method using only forces and no moment. The improved method was verified by comparing it to accepted solutions for a finite-width, center-crack specimen subjected to uniaxial tension. Four graphite/epoxy laminates were used: (0 + or - 45/90)sub s, (0), (+ or - 45)sub s, and (+ or - 30)sub s. The BFM results agreed well with accepted solutions. Convergence studies showed that with the addition of the moment in the fundamental solution, the number of boundary elements required for a converged solution was significantly reduced. Parametric studies were done for two configurations for which no orthotropic solutions are currently available; a single edge crack and an inclined single edge crack.
The Boundary Force Method (BFM), a form of indirect boundary element method, is used to analyze composite laminates with cracks. The BFM uses the orthotropic elasticity solution for a concentrated horizontal and vertical force and a moment applied at a point in a cracked, infinite sheet as the fundamental solution. The necessary stress functions for this fundamental solution were formulated using the complex variables theory of orthotropic elasticity. The current method is an improvement over a previous method using only forces and no moment. The improved method was verified by comparing it to accepted solutions for a finite-width, center-crack specimen subjected to uniaxial tension. Four graphite/epoxy laminates were used: (0 + or - 45/90)sub s, (0), (+ or - 45)sub s, and (+ or - 30)sub s. The BFM results agreed well with accepted solutions. Convergence studies showed that with the addition of the moment in the fundamental solution, the number of boundary elements required for a converged solution was significantly reduced. Parametric studies were done for two configurations for which no orthotropic solutions are currently available; a single edge crack and an inclined single edge crack.
This article explains results developed from the following research: 'The Stability of Plates and Shells beyond the Elastic Limit.' A significant improvement is found in the derivation of the relations between the stress factors and the strains resulting from the instability of plates and shells. In a strict analysis, the problem reduces to the solution of two simultaneous nonlinear partial differential equations of the fourth order in the deflection and stress function, and in the approximate analysis to a single linear equation of the Bryan type. Solutions are given for the special cases of a rectangular plate buckling into a cylindrical form, and of an arbitrarily shaped plate under uniform compression. These solutions indicate that the accuracy obtained by the approximate method is satisfactory.
This paper considers a sufficiently thin shallow shell of nonzero Gaussian curvature. It also presents a system of symmetrically constructed differential equations, constructed by the mixed method through the stress function and the displpacement function.
The general equations of equilibrium of a rotationally symmetrical body undergoing large arbitrary deflections but small strains are derived by means of the principle of virtual work. All deflections are referred to a reference surface which, in general, may be taken to coincide with any intermediate state of the membrane. Static solutions of the general equations for steadily rotating membranes are considered for the cases in which the final or the initial configuration of the membrane is specified. For problems in which the final configuration is specified, conditions are given under which such a configuration is obtainable from a stress-free initial state. Such conditions being satisfied, it is shown that the stresses and radial displacements are determinate while axial displacements may be obtained by quadrature. For problems in which the initial configuration is given, the determination of the stresses and deflections is reduced to the solution of a second-order nonlinear differential equation for a stress function. An approximate method of solution based on boundary-layer considerations is presented for the case of a spinning sphere of constant thickness. Specific examples are given for both classes of problems.
The plane-stress equations of linear elasticity are used in conjunction with those of the boundary element method to develop a novel curved, quadratic boundary element applicable to structures composed of anisotropic materials in a state of plane stress or plane strain. The curved boundary element is developed to solve two-dimensional, elastostatic problems of arbitrary shape, connectivity, and material type. As a result of the anisotropy, complex variables are employed in the fundamental solution derivations for a concentrated unit-magnitude force in an infinite elastic anisotropic medium. Once known, the fundamental solutions are evaluated numerically by using the known displacement and traction boundary values in an integral formulation with Gaussian quadrature. All the integral equations of the boundary element method are evaluated using one of two methods: either regular Gaussian quadrature or a combination of regular and logarithmic Gaussian quadrature. The regular Gaussian quadrature is used to evaluate most of the integrals along the boundary, and the combined scheme is employed for integrals that are singular. Individual element contributions are assembled into the global matrices of the standard boundary element method, manipulated to form a system of linear equations, and the resulting system is solved. The interior displacements and stresses are found through a separate set of auxiliary equations that are derived using an Airy-type stress function in terms of complex variables. The capabilities and accuracy of this method are demonstrated for a laminated-composite plate with a central, elliptical cutout that is subjected to uniform tension along one of the straight edges of the plate. Comparison of the boundary element results for this problem with corresponding results from an analytical model show a difference of less than 1%.
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.
Model‐based estimates of soil moisture (SM)‐evapotranspiration (ET) coupling strength(ρ) vary widely and are prone to bias. Here we apply numerical modeling and remote sensing to identify the process‐level source of modeledρbias with the goal of improving the fidelity of current Earth system models. Results illustrate that modeledρis most strongly determined by soil evaporation (E) stress, and (generally positive)ρmodeling bias is attributable to the oversimplification of soil texture impacts on E stress. Based on new remotely sensed estimates ofρ, we demonstrate that removingρbias via a single optimized E stress parameter leads to improved ET accuracy and resolves a well‐known modeling bias in the partitioning of ET into E and T. As such, we highlight the importance of the stress function relating E and SM and its central role in regulating land‐atmosphere coupling processes impacting local climate.
Stress intensity factors for quarter-elliptical corner cracks emanating from a circular hole are determined using a 3-D weight function method combined with a 3-D finite element method. The 3-D finite element method is used to analyze uncracked configuration and provide stress distribution in the region where crack is to occur. Using this stress distribution as input, the 3-D weight function method is used to determine stress intensity factors. Three different loading conditions, i.e. remote tension, remote bending and wedge loading, are considered for a wide range in geometrical parameters. The significance in using 3-D uncracked stress distribution and the difference between single and double corner cracks are studied. Typical crack opening displacements are also provided. Comparisons are made with solutions available in the literature.
Parallel with the work in Part-1, stress intensity factors for semi-elliptical surface cracks emanating from a circular hole are determined. The 3-D weight function method with the 3D finite element solutions for the uncracked stress distribution as in Part-1 is used for the analysis. Two different loading conditions, i.e. remote tension and wedge loading, are considered for a wide range in geometrical parameters. Both single and double surface cracks are studied and compared with other solutions available in the literature. Typical crack opening displacements are also provided.
Spaceflight factors, such as microgravity and space radiation, are known to put astronauts at risk for negative effects to their tissue regeneration and degenerative conditions. On our previous spaceflight research, we found that long duration spaceflight produced increased oxidative stress and activation of the inflammatory response as a major contributor to physiological changes, including alterations to the cardiovascular and musculoskeletal systems, metabolism, and the liver. Proliferation, apoptosis, and ion-channel remodeling of vascular smooth muscle cells, as well as endothelial inflammation, and nitric oxide synthase-nitric oxide system regulation have been shown by spaceflight and simulated spaceflight projects. CDKN1ap21 is a regulatory gene for tissue regeneration and also plays an important role in upregulating oxidative stress caused by radiation. In further research, we have also determined CDKN1ap21 to be overexpressed during spaceflight. When knocked out in mice, however, it protects against unloading-induced changes to the morphology and physiology of carotid arteries. In this proposal, we seek to test a potential dietary countermeasure to down-regulate CDKN1ap21 in the mice and protect against oxidative stress in the rodents. Specifically, we will expose both Wildtype and CDKN1ap21-null mice to hydrogen peroxide to induce oxidative stress and observe the molecular mechanisms in which a dietary supplement protects vascular smooth muscle cells against the consequences of the apoptotic environment within Wildtype mice versus the, hypothetically, sound physiology of CDKN1ap21-null mice. The successful completion of this experiment will conclusively determine accuracy of a dietary supplement as a CDKN1ap21 suppressor. This will provide a new perspective on the problem of increased oxidative stress developing into cardiovascular disease as a result of long-term space flight. This research will address the Human Research Plan Roadmaps Risk of Cardiac Rhythm Problems including CV-8, the Risk of Cardiovascular Disease and Other Degenerative Tissue Effects from Radiation Exposure including Degen-6 and Degen-7, and the Risk of Adverse Health Event from Radiation Exposure including IM-8. Additionally, this research will address Space Biology Research Plans questions SBP CMB-1, SBP CMB-3, and SB AN-2.
Broad tissue degeneration and the failure of normal tissue regenerative processes in microgravity because of mechanical unloading are increasing concerns for sustaining life in space as the duration of future flight missions increases. Work in our laboratory has identified normal adult stem cell-based tissue regenerative processes, such as the formation of new bone, cartilage, and immune cells, as being particularly sensitive to the stresses of mechanical unloading in microgravity. Our studies have also identified the inhibition of differentiation of marrow mesenchymal stem cells and activation of CDKN1ap21-mediated cell cycle arrest in proliferative osteoprecursor cells on the bone surface as potential mechanisms for spaceflight-induced skeletal changes. This finding, in combination with the role of CDKN1ap21 as a suppressor of mammalian tissue regeneration, suggests that this gene could be responsible for suppressing stem cell-based tissue regeneration in response to disuse. In this work, we hypothesized that CDKN1ap21 regulates regenerative bone formation in response to alterations in mechanical load and tested this hypothesis by studying the skeletal phenotype and stem cell regenerative ability of juvenile (4-11 weeks old) and adult (18 weeks-12 months old) p21 (--) knockout (KO) mice. Additionally, we analyzed bone micro-architectural properties, bone formation rates and differentiation capacity of bone marrow stem cells (BMSCs) from male and female KO mice exposed to hindlimb unloading (HU) for 15-30 days. We found that juvenile KO mice exhibited increased femoral trabecular and cortical bone formation, whilst three-point bending of the tibias from KO mice showed decreased bone stiffness. Conversely, adult KO mice exhibited no significant differences in micro-architectural properties compared to WT (wild-type) but woven bone structure was indicative of rapid bone remodeling. Furthermore, cortical bone properties showed similar characteristics to aged bone, including increased cross-sectional area and perimeter, whilst three-point bending showed increased stiffness and toughness. Interestingly, in-vitro, KO mice exhibited increased differentiation and mineralized nodule formation in osteoblastogenesis assays compared to WT. Preliminary results from CDKN1ap21 KO mice subjected to HU suggest altered sensitivity to mechanical unloading resulting in decreased cortical thickness compared to WT mice. However, KO mice subjected to short and long-duration HU show increased in-vitro differentiation potential of BMSCs to from form mature, mineral-forming osteoblasts, indicating maintenance of regenerative potential. Analysis of bone formation rates, cell proliferation rates and key genes of interest are currently underway. These results indicate a novel role for CDKN1ap21 in load-dependent osteoprogenitor proliferation and differentiation and that deletion of CDKN1ap21 results in an age-dependent release of osteoblast proliferation inhibition and increased bone formation and turnover.