Search NASA⌕ Search

Engineering topics

Gallagher, R. H.

Publications and source records attributed to Gallagher, R. H..

17 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1991

Compatibility conditions of structural mechanics for finite element analysis

The equilibrium equations and the compatibility conditions are fundamental to the analyses of structures. However, anyone who undertakes even a cursory generic study of the compatibility conditions can discover, with little effort, that historically this facet of structural mechanics had not been adequately researched by the profession. Now the compatibility conditions (CC's) have been researched and are understood to a great extent. For finite element discretizations, the CC's are banded and can be divided into three distinct categories: (1) the interface CC's; (2) the cluster or field CC's; and (3) the external CC's. The generation of CC's requires the separating of a local region, then writing the deformation displacement relation (ddr) for the region, and finally, the eliminating of the displacements from the ddr. The procedure to generate all three types of CC's is presented and illustrated through examples of finite element models. The uniqueness of the CC's thus generated is shown.

Patnaik, S. N.↗
NASA NTRS1991

Integrated force method versus displacement method for finite element analysis

A novel formulation termed the integrated force method (IFM) has been developed in recent years for analyzing structures. In this method all the internal forces are taken as independent variables, and the system equilibrium equations (EEs) are integrated with the global compatibility conditions (CCs) to form the governing set of equations. In IFM the CCs are obtained from the strain formulation of St. Venant, and no choices of redundant load systems have to be made, in constrast to the standard force method (SFM). This property of IFM allows the generation of the governing equation to be automated straightforwardly, as it is in the popular stiffness method (SM). In this report IFM and SM are compared relative to the structure of their respective equations, their conditioning, required solution methods, overall computational requirements, and convergence properties as these factors influence the accuracy of the results. Overall, this new version of the force method produces more accurate results than the stiffness method for comparable computational cost.

Patnaik, S. N.↗
NASA NTRS1977

Instability analysis of torispherical pressure vessel heads with triangular thin-shell finite elements

The elastic instability of an internally-pressurized cylindrical tank with a torispherical head is investigated using a triangular, doubly curved, thin-shell finite element. The formulation of the finite element, which is based upon cubic displacement functions and a modified principle of potential energy, is first described. Then, the element is verified by comparing numerical results for the linear, stable analysis to alternative solutions for the same problem. The subsequent instability investigation includes the solution of the linearized problem of equilibrium bifurcation, that is, of the classical eigenvalue problem, and a general nonlinear analysis, based on tracing the nonlinear load-displacement path. The critical pressure, obtained with use of the general nonlinear analysis, agrees closely with an experimental result as well as with a numerical solution stemming from an axisymmetric formulation.

Kanodia, V. L.↗
NASA NTRS1976

Finite element representations for thin shell instability analysis

The development of finite element calculational procedures for thin-shell instability analysis has involved the definition of appropriate element representations (i.e. the geometric form of the element and the approximation of displacement and/or stress), constitutive expressions, and computational algorithms. Among these, the status of thin-shell finite element representations remains unsettled. This paper, therefore, emphasizes recent developments in the basic aspects of thin-shell finite element analysis and discusses one simplified approach in more detail. Formulative and computational procedures for elastic instability analysis are then summarized, and numerical results are shown for the simplified shell element formulation.

Gallagher, R. H.↗
NASA NTRS1976

A triangular element based on generalized potential energy concepts

Stiffness equations are formulated for a doubly-curved triangular thin shell finite element. The strain energy component of the potential energy is first expressed in terms of displacements and displacement gradients with the aid of consistent deep shell strain-displacement equations. The element in-plane and normal displacement fields are approximated by complete cubic polynomials. These functions do not satisfy the interelement displacement admissibility conditions. Satisfaction is forced by the imposition of constraint conditions on the interelement boundaries; the constraints represent the modification of the potential energy. Some numerical results for a pinched cylinder, a cylindrical sphere, and a pinched sphere are examined.

Thomas, G. R.↗
NASA NTRS1975

A triangular thin shell finite element: Linear analysis

The formulation of the linear stiffness matrix for a doubly-curved triangular thin shell element, using a modified potential energy principle, is described. The strain energy component of the potential energy is expressed in terms of displacements and displacement gradients by use of consistent Koiter strain-displacement equations. The element inplane and normal displacement fields are approximated by complete cubic polynomials. The interelement displacement admissibility conditions are met in the global representation by imposition of constraint conditions on the interelement boundaries; the constraints represent the modification of the potential energy. Errors due to the nonzero strains under rigid body motion are shown to be of small importance for practical grid refinements through performance of extensive comparison analyses.

Thomas, G. R.↗
NASA NTRS1975

A triangular thin shell finite element: Nonlinear analysis

Aspects of the formulation of a triangular thin shell finite element which pertain to geometrically nonlinear (small strain, finite displacement) behavior are described. The procedure for solution of the resulting nonlinear algebraic equations combines a one-step incremental (tangent stiffness) approach with one iteration in the Newton-Raphson mode. A method is presented which permits a rational estimation of step size in this procedure. Limit points are calculated by means of a superposition scheme coupled to the incremental side of the solution procedure while bifurcation points are calculated through a process of interpolation of the determinants of the tangent-stiffness matrix. Numerical results are obtained for a flat plate and two curved shell problems and are compared with alternative solutions.

Thomas, G. R.↗
NASA NTRS1974

Shear buckling of square perforated plates

The behavior of thin square perforated plates under the action of uniform shear deformation is studied experimentally and analytically using finite element analysis. Elastic Shear buckling strength is established as a function of the diameter of a round, centrally located hole in the plate. Post buckling behavior and the behavior of perforated plates with various ring stiffeners are also studied experimentally.

Grosskurth, J. F., Jr.↗
NASA NTRS1973

The finite element method in shell stability analysis.

A development of the finite element method for thin shell instability analysis is presented, covering three principal aspects: (1) representation of shell geometry, (2) representation of element behavior, and (3) algorithmic tools for solution of the large-order systems of nonlinear algebraic equations which characterize various phases of shell instability. Two shell elements are described, an arbitrary quadrilateral and a triangle, and numerical results are presented for two widely-employed comparison problems for linear (stable) analysis. Two shell problems which include instability effects are also solved.-

Gallagher, R. H.↗
NASA NTRS1973

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.↗
NASA NTRS1972

A method of limit point calculation in finite element structural analysis

An approach is presented for the calculation of limit points for structures described by discrete coordinates, and whose governing equations derive from finite element concepts. The nonlinear load-displacement path of the imperfect structure is first traced by use of a direct iteration scheme and the determinant of the governing algebraic equations is calculated at each solution point. The limit point is then established by extrapolation and imposition of the condition of zero slope of the plot of load vs. determinant. Three problems are solved in illustration of the approach and in comparison with alternative procedures and test data.

Gallagher, R. H.↗
NASA NTRS1972

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.↗