Composite FEM Analysis for Layered Systems
Publication: Journal of Engineering Mechanics
Volume 110, Issue 9
Abstract
A composite characterization and accompanying finite element analysis for layered systems is presented. The model is developed for plane strain and axisymmetric (horizontal layers) configurations with stiff, relatively thin isotropic layers of reinforcement sandwiched between layers of relatively flexible isotropic matrix material. Potential applications include elastomeric bearings and reinforced earth structures. The composite theory, in addition to capturing the overall response characteristics of the layered system, approximately models the important edge effects which occur at boundaries and the stress concentrations at layer interfaces. The primary dependent variables for the composite theory have been selected such that the highest derivatives appearing in the strain energy function are first order, thus requiring only continuity of the finite element approximations. As a result, the accompanying finite analysis is simple and computationally efficient. Numerical examples are presented to verify the theory, compare it to previous results, and to illustrate potential applications of the analysis.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Brown, B. B., “Design of Fabric Reinforced Retaining Structures” Proceedings of Symposium on Earth Reinforcement, ASCE, Apr., 1978.
2.
Clark, E. V., and Moultrop, K., “Load‐Deformation Characteristics of Elastomeric Bridge Bearing Pads,” Highway Research Record, Vol. 34, 1963.
3.
Derham, C. J., and Thomas, A. G., “The Design and Use of Rubber Bearings for Vibration Isolation and Seismic Protection of Structures,” Engineering Structures, Vol. 2, No. 3, July, 1980.
4.
“Development of an Elastomeric Seal for Omniaxial Movable Nozzles (Lock‐seal),” Technical Report No. AFRPL‐TR‐66‐112, Lockheed Propulsion Co., 1966.
5.
Eringen, A. C., “Linear Theory of Micropolar Elasticity,” Journal Math, and Mech., Vol. 15, No. 2, 1966.
6.
Gent, A. N., and Meinecke, E. A., “Compression, Bending and Shear of Bonded Rubber Blocks,” Polymer Engineering and Science, Vol. 10, No. 1, Jan., 1970.
7.
Gent, A. N., Henry, R. L., and Roxbury, M. L., “Interfacial Stresses for Bonded Rubber Blocks in Compression and Shear,” Transactions, Journal of Applied Mechanics, ASME, Vol. 41, No. 4, Dec., 1974.
8.
Herrmann, L. R., “Elasticity Equations for Incompressible and Nearly Incompressible Materials by a Variational Theorem,” AIAA Journal, Vol. 3, No. 10, Oct., 1965.
9.
Herrmann, L. R., “Interpretation of Finite Element Procedure as Stress Error Minimization Procedure,” Journal of the Engineering Mechanics Division, ASCE, No. EM5, Oct., 1972.
10.
Herrmann, L. R., “Finite Element Modeling of Composite Edge Effects,” presented at the August, 1979, ASCE 7th Conference on Electronic Computations, held at St. Louis, Mo.
11.
Herrmann, L. R., “Mixed Finite Elements for Couple‐Stress Analysis,” Proceedings, International Symposium on Hybrid and Mixed Finite Element Methods, Apr., 1981.
12.
Herrmann, L. R., and Al‐Yassin, Z., “Numerical Analysis of Reinforced Soil Systems,” Proceedings of Symposium on Earth Reinforcement, ASCE Apr., 1978.
13.
Herrmann, L. R., and Schamber, R. A., “Finite Element Analysis of Layered Systems with Edge Effects,” Numerical Methods for Coupled Problems, E. Hinton, P. Bettess, R. W. Lewis, eds., Pineridge Press, Swansea, United Kingdom, 1981.
14.
Kulkarni, S., B., “Design Criteria for Elastomeric Bearings, Volume II—Design Manual,” Thiokol/Wasatch Division, AD/A‐024767, Mar., 1976.
15.
Lindley, P. B., and Teo, S. C., “Some Numerical Stiffnesses of Soft Elastic Blocks Bonded to Rigid End Plates,” Plastics and Rubber: Materials Applications, Aug., 1978.
16.
Moore, J. K., and Herrmann, L. R., “A Stress‐Strain Analysis of Rubber and Steel Composite Bearings,” Proceedings of the 4th Engineering Mechanics Division Specialty Conference on Recent Advances in Engineering Mechanics and Their Impact on Civil Engineering Practice, ASCE Vol. 2, May, 1983.
17.
Nayfeh, A. H., Perturbation Methods, John Wiley and Sons, New York, N.Y., 1973.
18.
Pagano, N. J., “Stress Fields in Composite Laminates,” International Journal of Solids and Structures, Vol. 14, 1978.
19.
Rejcha, C., “Design of Elastomer Bearings,” PCI Journal, Vol. 9, No. 2, Oct., 1964.
20.
Schamber, R. A., “Plane Strain Composite Analysis Including Edge Effects of Layered Systems,” thesis presented to the University of California, at Davis, Calif., in partial fulfillment of the requirements for the degree of Masters of Science.
21.
Soni, M. L., “A Microstructure Continuum Theory for Laminated Elastic Composites,” thesis presented to the University of Texas, at Austin, Tex., in 1966, in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
22.
Sun, C. T., Achenbach, J. D., and Herrmann, G., “Continuum Theory for a Laminated Medium,” J.A.M., Vol. 35, 1968.
23.
Stanton, J. F., and Roeder, C. W., “Elastomeric Bearings Design, Construction and Materials,” Report 248, National Cooperative Highway Research Program, 1982.
24.
Tsai, S. W., and Hahn, H. T., Introduction to Composite Materials, Technomic Publishing Co., Westport, Conn., 1980.
25.
Wang, A. S. D., and Crossman, F. W., “Calculation of Edge Effects in Multi‐Layer Laminates by Sub‐Structuring,” Journal of Composition Materials, Vol. 12, Jan., 1978.
26.
Wang, S. S., and Choi, I., “Boundary‐Layer Effects in Composite Laminates,” JAM, Vol. 49, 1982.
27.
Welch, K., “Analysis of Axisymmetric Layered Systems Including Edge Effects,” thesis presented to the University of California, at Davis, Calif., in 1981, in partial fulfillment of the requirements for the degree of Master of Science.
Information & Authors
Information
Published In
Copyright
Copyright © 1984 ASCE.
History
Published online: Sep 1, 1984
Published in print: Sep 1984
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.