K. Satyamurthy

Consistent finite element procedures for nonlinear rubber elasticity with a higher order strain energy function

Abstract The use of higher order terms in the Rivlins polynomial strain energy density function is necessary to describe the elastic behavior of rubber undergoing very large and complex deformation. In this paper, the material response tensor for general Rivlins strain energy density function is derived in a consistent manner such that both major and minor symmetries are retained. Lack of minor symmetry in the material response tensor will lead to numerical convergence difficulties, especially in shear dominant problems. The projection method is used to avoid volumetric locking due to the nearly incompressible nature of rubber. The relation between the numerical penalty number and the material bulk modulus is characterized. The importance of this relation is demonstrated in the study of the apparent Youngs modulus of bonded rubber units. The need to include higher order terms in the strain energy density function is presented in the numerical examples. Several classical elasticity problems are also analyzed.

Finite Element Modeling of a Homogeneous Pneumatic Tire Subjected To Footprint Loadings

Abstract In this paper, we use an approach which involves 3D finite elements and a contact algorithm. For a given deflection of the hub, the algorithm computes the nodes that come into contact with a predefined contact plane, and the magnitudes of the contact forces at the nodes. Thus, the algorithm computes the size and shape of the footprint, and the contact forces at the FE nodes. To illustrate the technique, we analyze a homogeneous tire subjected to footprint loading. The computed shapes and sizes of the footprint area at different levels of rim deflection are shown to be in good agreement with experimental results. The computed tire profiles and the load‐deflection response of the tire are also in good agreement with experimental results. The computed results include the distribution of stress, strain, and strain energy density within the tire, and the changes in this distribution with applied footprint loadings.

An Efficient Approach for the Three‐Dimensional Finite Element Analysis of Tires

The finite element analysis of tires under a vertical footprint load requires the use of three-dimensional models. The excessive CPU time required for such models, especially when the tire construction is considered in detail, makes parametric studies difficult and time-consuming. Therefore, one of the principal objectives of finite element program development is to provide an efficient tool for the three-dimensional analysis of tires so that it can be integrated into the design process effectively. In the present study, a systematic finite element procedure is developed for solving loaded tire problems. The principal elements of this procedure are an efficient pre-processor for input generation, a multipoint constraint option to allow the user to exploit any existing symmetry in the problem, and a procedure for generating initial conditions from axisymmetric analyses. This procedure can be used to conduct parametric studies on loaded tires by using a rather coarse mesh and large load steps, thus leading to a significant reduction in CPU time, with a minimum sacrifice in solution accuracy. The efficiency of this procedure is illustrated with the analysis of a radial automobile tire.

An automated, energy-based, finite-difference procedure for the elastic collapse of rectangular plates and panels

Abstract A FORTRAN IV, large capacity, computer program has been developed to determine collapse loads and bifurcation loads for linear and nonlinear prebuckling behavior for fiber-reinforced, laminated, rectangular plates and panels under general loading systems and boundary conditions. The program is based on the principle of total potential energy and uses finite-differences in the discretization process. Whole-station spacing has been used to calculate the strain energy associated with an area-element and an orthogonal finite-difference grid that provides for variable spacings in perpendicular directions is incorporated. Numerical results are presented that compare favorably with results obtained via the general computer program STAGS. Other numerical results are presented that illustrate the types of boundary conditions, applied loads, cut-outs and initial geometric imperfections that can be handled by the present program. A brief study of the effect of panel construction and initial geometric imperfections on the buckling behavior of fiber-reinforced panels is presented.

Contact Loading of a Rubber Disk

Abstract A computational method is described for the analysis of deformable bodies loaded against rigid surfaces. The deformable body is modeled by three‐dimensional isoparametric elements. A contact algorithm determines the nodes that come into contact with each loading step; the finite element analysis computes the size and shape of the footprint and the distribution of contact pressure in the footprint. The procedure is illustrated by analysis of the contact of a rubber disk. The close agreement, shown between the computed and measured results for the rubber disk, demonstrates the potential of the technique for 3D contact analysis of pneumatic tires.

Effect of Spatial Variation of Thermal Conductivity on Magnitude of Tensile Thermal Stresses in Brittle Materials Subjected to Convective Heating

The results are presented for the effect of spatially varying thermal conductivity on the tensile thermal stress developed in a solid and a hollow circular cylinder subjected to different heating conditions. It is shown that the maximum tensile thermal stress in brittle ceramics can be reduced significantly by redistributing the temperature profile using (a) a spatial variation in thermal conductivity, (b) a spatial variation in pore content which in turn changes the density, thermal conductivity and modulus of elasticity and (c) by considering the effect of temperature on the thermal conductivity and specific heat. Possible methods for creating such variations in the material properties are discussed.

An Axisymmetric Finite Element and Its Use to Examine the Effects of Construction Variables on Radial Tires

Abstract A nonlinear axisymmetric formulation has been developed which allows circumferential as well as radial and lateral displacements. Significant circumferential displacements occur in radial tires under an inflation load both in the crown region and in the sidewall of the tire. The model is used in this study to assess the types of deformations that occur and the effect of construction variables on these deformations. The variables considered include belt angle, belt width, belt edge filler modulus, and chafer angle. The effect of changes in these variables on both in‐plane and circumferential deformations, as well as cord loads and interply shear strains are reported. Wherever possible the numerical results are compared with experimental measurements. Predicted deformations due to chafer orientations were sometimes unexpected, but were confirmed by experiment.