Mode matching method for anisotropic guides.
Mode-matching technique for bifurcated anisotropic waveguide, discussing Bresler biorthogonality relationships to derive anisotropic guide mode equations
MODE SHAPE↗
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Buckling of shells of revolution with various wall constructions. Volume 2 - Basic equations and method of solution
Basic equations and method of solution for computerized analysis of shells of revolution with axisymmetric collapse and nonsymmetric bifurcation buckling behavior
Almroth, B. O.↗
An analysis of the coupled chemically reacting boundary layer and charring ablator. Part 4 - A unified approximation for mixture transport properties for multicomponent boundary-layer applications
Bifurcation approximation for binary and thermal diffusion coefficients, mixture viscosity, and thermal conductivity of laminar boundary layer
Bartlett, E. P.↗
Response of the perfused carotid body to changes in pH and P sub CO2.
Carotid bifurcation of cats perfused at constant pressures with bicarbonate buffered Ringer solution, discussing chemoreceptor responses to pH and carbon dioxide pressure
Gray, B. A.↗
Periodic solutions of differential equations with time lag containing a small parameter.
Periodic solutions for functional differential equations with time lag, developing bifurcation theory representing delay equation extension
Perello, C.↗
On the postbuckling behavior of imperfection- sensitive structures in the plastic range
Plastic postbuckling and imperfection sensitivity of spherical shells under axisymmetric bifurcation
Hutchinson, J. W.↗
The Afar triple junction and sea-floor spreading
Critique of Ethiopian Afar depression formation as oceanic crust resulting from Arabia drift, considering plate tectonics analysis for bifurcated spreading zones
Mohr, P. A.↗
Computer program for analysis of imperfection sensitivity of ring stiffened shells of revolution
A FORTRAN 4 digital computer program is presented for the initial postbuckling and imperfection sensitivity analysis of bifurcation buckling modes for ring-stiffened orthotropic multilayered shells of revolution. The boundary value problem for the second-order contribution to the buckled state was solved by the forward integration technique using the Runge-Kutta method. The effects of nonlinear prebuckling states and live pressure loadings are included.
Cohen, G. A.↗
A finite element procedure for nonlinear prebuckling and initial postbuckling analysis
A procedure cast in a form appropriate to the finite element method is presented for geometrically nonlinear prebuckling and postbuckling structural analysis, including the identification of snap-through type of buckling. The principal features of this procedure are the use of direct iteration for solution of the nonlinear algebraic equations in the prebuckling range, an interpolation scheme for determination of the initial bifurcation point, a perturbation method in definition of the load-displacement behavior through the postbuckling regime, and extrapolation in determination of the limit point for snap-through buckling. Three numerical examples are presented in illustration of the procedure and in comparison with alternative approaches.
Mau, S. T.↗
A digital computer study of the buckling of shallow spherical caps and truncated hemispheres
A study of the buckling of thin shells was conducted using a digital computer program for the geometrically nonlinear analysis of arbitrarily loaded shells of revolution. The objective was an evaluation of the program's applicability to bifurcation buckling and imperfection sensitivity analysis. Clamped spherical caps under pressure loading and clamped truncated hemispheres under axial tension were investigated. Buckling loads were determined for axisymmetric and nearly axisymmetric loads and are compared with previously published analytical results based on geometric imperfections.
Stilwell, W. C.↗
Buckling of circular cylindrical shells under axial compression.
The infinitely long cylindrical shell under axial compression with axisymmetric sinusoidal imperfections is considered. The bifurcation problem is formulated exactly, and a complete family of buckling modes is identified. Koiter's (1963) upper bound pertains to the critical stress associated with one restricted set of modes, and the critical stress for a set of long wavelength modes reproduces some numerical results obtained by Almroth (1966). The initial postbuckling analysis is also formulated exactly. An exact analytical solution is obtained for the limiting case of modes with infinitely long wavelengths, and numerical analysis is used to solve the equations for the other cases. An appendix gives the details of the analysis.
Budiansky, B.↗
High speed flow past wings
The analytical solution to the transonic small perturbation equation which describes steady compressible flow past finite wings at subsonic speeds can be expressed as a nonlinear integral equation with the perturbation velocity potential as the unknown function. This known formulation is substituted by a system of nonlinear algebraic equations to which various methods are applicable for its solution. Due to the presence of mathematical discontinuities in the flow solutions, however, a main computational difficulty was to ensure uniqueness of the solutions when local velocities on the wing exceeded the speed of sound. For continuous solutions this was achieved by embedding the algebraic system in an one-parameter operator homotopy in order to apply the method of parametric differentiation. The solution to the initial system of equations appears then as a solution to a Cauchy problem where the initial condition is related to the accompanying incompressible flow solution. In using this technique, however, a continuous dependence of the solution development on the initial data is lost when the solution reaches the minimum bifurcation point. A steepest descent iteration technique was therefore, added to the computational scheme for the calculation of discontinuous flow solutions. Results for purely subsonic flows and supersonic flows with and without compression shocks are given and compared with other available theoretical solutions.
Norstrud, H.↗
Finite element formulations for problems of large elastic-plastic deformation
An Eulerian finite element formulation is presented for problems of large elastic-plastic flow. The method is based on Hill's variational principle for incremental deformations, and is suited to isotropically hardening Prandtl-Reuss materials. The formulation is given in a manner which allows any conventional finite element program, for "small strain" elasticplastic analysis, to be simply and rigorously adapted to problems involving arbitrary amounts of deformation and arbitrary levels of stress in comparison to plastic deformation moduli. The method is applied to a necking bifurcation analysis of a bar in plane-strain tension. A unified general formulation of finite element equations, both Lagrangian and Eulerian, for large deformations, with arbitrary choice of the conjugate stress and strain measures, and a discussion is given of other proposed formulations for elastic-plastic finite element analysis at large strain.
Mcmeeking, R. M.↗
Buckling of conical shell with local imperfections
Small geometric imperfections in thin-walled shell structures can cause large reductions in buckling strength. Most imperfections found in structures are neither axisymmetric nor have the shape of buckling modes but rather occur locally. This report presents the results of a study of the effect of local imperfections on the critical buckling load of a specific axially compressed thin-walled conical shell. The buckling calculations were performed by using a two-dimensional shell analysis program referred to as the STAGS (Structural Analysis of General Shells) computer code, which has no axisymmetry restrictions. Results show that the buckling load found from a bifurcation buckling analysis is highly dependent on the circumferential arc length of the imperfection type studied. As the circumferential arc length of the imperfection is increased, a reduction of up to 50 percent of the critical load of the perfect shell can occur. The buckling load of the cone with an axisymmetric imperfections is nearly equal to the buckling load of imperfections which extended 60 deg or more around the circumference, but would give a highly conservative estimate of the buckling load of a shell with an imperfection of a more local nature.
Cooper, P. A.↗
Behavior near constant solutions of functional differential equations
Techniques have been developed to determine in a systematic way the local behavior near constant solutions. Local integral manifolds play a very important role in this development, as they have also for ordinary differential equations. An attempt is made to indicate a few more applications of these methods to some problems in bifurcation in the spirit of Sotomayor (to appear) and to a growth model of Cooke and Yorke (to appear). It is also shown how to prove a theorem on stability under constantly acting disturbances using these methods.
Hale, J. K.↗
Finite element analysis of geometrically nonlinear problems
Recent developments in geometrically nonlinear finite element analysis are reviewed. Following a discussion of the theoretical bases for the construction of finite element equations for geometrically nonlinear analysis, the algorithmic tools for solving the resulting nonlinear equations of the complete system are described. Separate consideration is given to preinstability nonlinear analysis, the calculation of limit points, bifurcation points, and to postbifurcation analysis.
Gallagher, R. H.↗
Buckling of cylindrical shells with random imperfections
Buckling of long cylindrical shells with random imperfections subjected to axial loads is treated using the method of truncated hierarchy. A system of homogeneous variational equations is set up to examine the existence of bifurcation in the neighborhood of the equilibrium state. These equations are linear and involve stationary random coefficients. The truncated-hierarchy method is applied, and characteristic equations are obtained. Various exponential cosine correlation functions associated with asymmetric imperfections are examined numerically. Qualitatively, the results obtained are as anticipated.
Fersht, R. S.↗
Program for analysis of nonlinear equilibrium and stability (PANES)
PANES utilizes improved techniques for analysis of structures with material and geometric nonlinearities, including limit point and bifurcations behavior which occurs in buckling and collapse problems. Incremental loading, Newton-Raphson iteration, and higher order methods are used in program.
Vos, R. G.↗