# Finite Element Analysis of Hyperbolic Paraboloid Shells

Transition from Circular to Rectangular Section

*Two methods are widely used for the design of transitions from circular to rectangular box sections. One method is based on a straight line variation of area between the circular section...*

Simulation of Waves by an Underwater Explosion

*The properties of water waves produced by underwater explosions were studied in a test basin where the underwater disturbance was simulated by means of a rapidly withdrawn or immersed...*

Finite Element Plate Bending Equilibrium Analysis

*For the problem of elastic plate bending, a finite element procedure based on the minimum of complementary energy principle is developed. Primary variable of the problem is the distribution...*

Base Moment for a Class of Linear Systems

*Contributions of the second and higher modes to the overturning moment at the base of any classical linear system whose fundamental mode is given by a straight line are shown to vanish...*

Edge Effects in Hyperbolic Paraboloid Shells

*The influences of edge constraint upon the behaviour of single panel ruled surface hyperbolic paraboloids with straight generator boundaries are studied. With apex and base corners clamped...*

Convergence of Hypar Finite-Difference Solutions

*A study of the convergence rates of finite-difference solutions of the linear thin shallow shell equations for single panel ruled surface hyperbolic paraboloids is reported. Boundary conditions...*

Stability of Columns Subject to Impulsive Loading

*The stability criterion developed for simply supported columns determine a bound on the transverse motion of the column relative to the amplitude and duration of a prescribed force pulse...*

The Unsymmetrical Vertical Parabola

*An unsymmetrical vertical curve is occasionally required in the geometric design of highways, particularly at interchanges. The usual procedure in such cases makes use of two parabolas...*

Unsteady Flows in Lines with Distributed Leakage

*Unsteady, nonuniform flows in pipelines which experience leakage are analyzed. Particular attention is given to the orifice manifold. Plows in a continuous manifold can be treated in several...*

Design and Testing of Cone and Hypar Footing

*Model cone and hyperbolic paraboloid footings were tested to observe membrane and bending stresses and to measure soil pressure distributions under the footings. Variations in pressure...*

Stress Analysis of Translational Shells

*A set of governing simultaneous partial differential equations describing the bending and membrane stress conditions in any translational shell are derived in this study. By employing...*

Hyperbolic Paraboloid Structures on Four Supports

*It is generally recognized that actual loading and construction details of hyperbolic paraboloid structures are far from ideal, and therefore incompatible with the membrane state of stress,...*

Single-Layer Corrugated-Steel-Sheet Hypars

*Vertical loading tests were conducted on several hyperbolic paraboloid (hypar) roofs fabricated from single layers of corrugated steel sheets: (1) A 4-ft-sq shell with rectangular corrugations;...*

Stresses and Deformations in Umbrella Shells

*Governing equations in the form of two, coupled, fourth-order partial differential equations are obtained from shallow shell theory. The equations are specialized for the hyperbolic paraboloid...*

Automatic Solution of Pucher's Equation

*The system of shell membrane force-equilibrium equations expressed in terms of cartesian coordinates can be reduced to a single differential equation, called Pucher's equation,...*

Bending of Hyperbolic Paraboloid Structures

*Deformations and internal forces in the edge members of square hyperbolic paraboloids on two supports are calculated herein. Results are based on the bending theory of shallow elastic...*

Analysis of Continuous Arch Frames

*The analysis of continuous arch frames with curved members of constant cross-section and either circular, parabolic or semi-elliptic arch form by means of an extension of the slope deflection...*

Homologous Deformations of Tiltable Telescopes

*The deformation of a structure is defined to be homologous if a given geometrical relation holds for a given number of structural points, before, during, and after the deformation. Applied...*

Characteristics on M1 Backwater Curves

*An analysis of M1 profiles with Froude number as a reference parameter is made. A total of 182 M1 profiles in rectangular, trapezoidal, triangular, and parabolic channels are studied....*

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