A new four‐node (non‐flat) general quadrilateral shell element for geometric and material non‐linear analysis is presented. The element is formulated using three‐dimensional continuum mechanics theory and it is applicable to the analysis of thin and thick shells. The formulation of the element and the solutions to various test and demonstrative example problems are presented and discussed.

http://web.mit.edu/kjb/www/Publications_Prior_to_1998/A_Continuum_Mechanics_Based_Four-Node_Shell_Element_for_General_Nonlinear_Analysis.pdf

A continuum mechanics based four‐node shell element for general non‐linear analysis

Adaptive dynamic relaxation algorithm for non-linear hyperelastic structures Part I. Formulation

SUMMARY The landing gear is an inevitable system for the aircraft. It absorbs the energy of the landing impact and carries the aircraft weight at all ground operations, including take off, taxiing, and towing. Numerical simulation has become an invaluable tool for the assessment of landing gear dynamics as well as of aircraft/landing gear interaction. This paper gives an overview of the landing gear requirements and illustrates landing gear operational conditions, i.e., the shimmy problem, the dynamics at touch down and at ground roll. Furthermore, three software packages used in the simulation of aircraft ground dynamics are presented. A look at flight simulators and landing gear test facilities follows. Finally, the possible application of controlled landing gears is discussed.

Aircraft Landing Gear Dynamics: Simulation and Control

The development of contact theories and numerical formula for various applications is a field which expands rapidly. This publication focuses on the rolling contact problem both for tire-road and wheel-rail contact. For the tire-road application a central problem is the modeling of the composite structure of the tire under internal pressure and axle load. One actual contact problem is the rolling on soft soil, which is discussed as the main application. In the wheel-rail case the contact area is much smaller and much more emphasis has been laid on the treatment of material changes, wear and creep phenomena. These approaches are discussed in detail as well as a more recent finite element formulation following the arbitrary Lagrange-Eulerian concept. Ideas about damage mechanisms finish the article.

Advanced Contact Mechanics–Road and Rail

The risk of hydroplaning and reduction of skid resistance are two major safety concerns in wet weathering traffic operations on highways and runways. The writers earlier developed an analytical computer model to simulate the phenomenon of hydroplaning. The simulation of wet-pavement skid resistance is analytically a more complex problem to handle than hydroplaning simulation. The present paper adopts a more elaborate theoretical approach and proposes an improved analytical computer model to simulate hydroplaning as well as the reduction of wet-pavement skid resistance as the sliding wheel speed increases. The theoretical formulation and development of a three-dimensional finite-element model based on solid mechanics and fluid dynamics is presented. The computed hydroplaning speeds by the proposed model were analyzed and verified against the well-known experimentally derived National Aeronautics and Space Administration (NASA) hydroplaning-speed equation. The analysis confirmed that the NASA equation is a special case of a general solution, and that it is applicable only to a specific range of tire footprint aspect ratios. An analysis of the decreasing trend of wet-pavement skid resistance with vehicle speed and its validation against measured experimental data will be the subject of another paper.

Wet-Pavement Hydroplaning Risk and Skid Resistance: Modeling

Advances and trends in the development of computational models for tires

A computational procedure is presented for the solution of frictional contact problems for aircraft tires. A Space Shuttle nose-gear tire is modeled using a two-dimensional laminated anisotropic shell theory which includes the effects of variations in material and geometric parameters, transverse-shear deformation, and geometric nonlinearities. Contact conditions are incorporated into the formulation by using a perturbed Lagrangian approach with the fundamental unknowns consisting of the stress resultants, the generalized displacements, and the Lagrange multipliers associated with both contact and friction conditions. The contact-friction algorithm is based on a modified Coulomb friction law. A modified two-field, mixed-variational principle is used to obtain elemental arrays. This modification consists of augmenting the functional of that principle by two terms: the Lagrange multiplier vector associated with normal and tangential node contact-load intensities and a regularization term that is quadratic in the Lagrange multiplier vector. These capabilities and computational features are incorporated into an in-house computer code. Experimental measurements were taken to define the response of the Space Shuttle nose-gear tire to inflation-pressure loads and to inflation-pressure loads combined with normal static loads against a rigid flat plate. These experimental results describe the meridional growth of the tire cross section caused by inflation loading, the static load-deflection characteristics of the tire, the geometry of the tire footprint under static loading conditions, and the normal and tangential load-intensity distributions in the tire footprint for the various static vertical loading conditions. Numerical results were obtained for the Space Shuttle nose-gear tire subjected to inflation pressure loads and combined inflation pressure and contact loads against a rigid flat plate. The experimental measurements and the numerical results are compared.

Computational Methods for Frictional Contact With Applications to the Space Shuttle Orbiter Nose-Gear Tire

Currently used techniques for tire contact analysis are reviewed. Discussion focuses on the different techniques used in modeling frictional forces and the treatment of contact conditions. A status report is presented on a new computational strategy for the modeling and analysis of tires, including the solution of the contact problem. The key elements of the proposed strategy are: (1) use of semianalytic mixed finite elements in which the shell variables are represented by Fourier series in the circumferential direction and piecewise polynomials in the meridional direction; (2) use of perturbed Lagrangian formulation for the determination of the contact area and pressure; and (3) application of multilevel iteration procedures and reduction techniques to generate the response of the tire. Numerical results are presented to demonstrate the effectiveness of a proposed procedure for generating the tire response associated with different Fourier harmonics.

Advances in contact algorithms and their application to tires

Analysis of aircraft tires via semianalytic finite elements

The Langley Research Center has recently upgraded the Landing Loads Track (LLT) to improve the capability of low-cost testing of conventional and advanced landing gear systems. The unique feature of the Langley Aircraft Landing Dynamics Facility (ALDF) is the ability to test aircraft landing gear systems on actual runway surfaces at operational ground speeds and loading conditions. A historical overview of the original LLT is given, followed by a detailed description of the new ALDF systems and operational capabilities.

John A. Tanner

Papers

Advances and trends in the development of computational models for tires

Computational Methods for Frictional Contact With Applications to the Space Shuttle Orbiter Nose-Gear Tire

Advances in contact algorithms and their application to tires

Analysis of aircraft tires via semianalytic finite elements

Langley Aircraft Landing Dynamics Facility