Transient Response of Laminated,Bimodular-Material,Composite Rectangular Plates

Abstract

The paper presents a finite-element analysis of the transient behavior of fiber-reinforced, single-layer and two-layer cross-ply rectangular plates of bimodular materials (i.e., materials whose linear elastic properties are dif ferent depending on whether the fiber-direction strains are tensile or com pressive). To validate the finite element results, a closed-form solution is also presented for a rectangular plate with all edges simply-supported without in- plane restraint (along the edge) and tangential rotation and subjected to sud denly applied sinusoidally distributed normal pressure. The time behavior of the transverse loading is arbitrary (e.g., step loading, impulse loading, etc.). Numerical results for transverse deflection and locations of the 'neutral sur face' as functions of time are presented for two bimodular materials. The finite element solutions agree very closely with the closed-form solutions.

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References

S. Timoshenko , Strength of Materials, Part II: Advanced Theory and Problems , 2nded., Van Nostrand, Princeton, NJ, 1941, pp. 362-369.

S.A. Ambartsumyan , "The Axisymmetric Problem of a Circular Cylindrical Shell Made of Material with Different Stiffnesses in Tension and Compression," Izvestiya Akademiya Nauk SSR, Mekhanika , No. 4, 1965, pp. 77-85; English translation, National Technical Information Center Document AD-785312 (1967).

N. Kamiya , "Transverse Shear Effect in a Bimodulus Plate," Nuclear Engineering and Design, Vol. 32, No. 3, 1975, pp. 351-357.

N. Kamiya , "An Energy Method Applied to Large Elastic Deformation of a Thin Plate of Bimodulus Material," Journal of Structural Mechanics , Vol. 3, No. 3, 1975, pp. 317-329.

N. Kamiya , "Thermal Stress in a Bimodulus Thin Plate," Bulletin de l'Academie des Sciences, Serie des Sciences Techniques, Vol. 24, 1976, pp. 365-372.

R.M. Jones and H.S. Morgan , "Bending and Extension of Cross-Ply Laminates with Different Moduli in Tension and Compression," Computers and Structures, Vol. 11, No. 3, 1980, pp. 181-190.

J.N. Reddy and C.W. Bert , "Analyses of Plates Constructed of Fiber-Reinforced Bimodulus Materials," Mechanics of Bimodulus Materials , C.W. Bert (ed.) AMD Vol. 33, ASME, NY, 1979, pp. 67-83.

C.W. Bert , V.S. Reddy , and S.K . Kincannon , "Deflection of Thin Rectangular Plates of Cross-plied Bimodulus Material," Journal of Structural Mechanics, Vol. 8, No. 4, 1980, pp. 347-364.

J.N. Reddy and W.C. Chao , "Finite-Element Analysis of Laminated Bimodulus Composite-Material Plates," Computers and Structures, Vol. 12, 1980 , pp. 245-251.

10.

J.N. Reddy , C.W. Bert , Y.S . Hsu , and Reddy, V.S. , "Thermal Bending of Thick Rectangular Plates of Bimodulus Composite Materials," Journal of Mechanical Engineering Science, Vol. 22, No. 6, 1980, pp. 297-304.

11.

C.W. Bert , J.N. Reddy , V.S . Reddy , and W.C . Chao , "Bending of Thick Rectangular Plates Laminated of Bimodulus Composite Materials," AIAA Journal, Vol. 19, No. 10, 1981, pp. 1342-1349.

12.

N.M. Newmark , "A Method of Computation for Structural Dynamics," ASCE Journal of the Engineering Mechanics Division , Vol. 85, EM3, 1959, pp. 67-94.

13.

J.M. Whitneyand N.J. Pagano , "Shear Deformation in Heterogeneous Anisotropic Composite Plates," ASME Journal of Applied Mechanics , Vol. 37, 1970, pp. 1031-1036.

14.

C.W. Bert , J.N. Reddy , W.C . Chao , and V.S . Reddy , "Vibration of Thick Rectangular Plates of Bimodulus Composite Material," ASME Journal of Applied Mechanica, Vol. 48, 1981, pp. 371-376.

15.

J.N. Reddy , "On the Solutions to Forced Motions of Layered Composite Plates," Research Report No. VPI-E-81-24, Department of Engineering Science and Mechanics, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061; ASME Journal of Applied Mechanics (to appear).

16.

T.Y. Tsui and P. Tong , "Stability of Transient Solution of Moderately Thick Plate by Fintie Difference Method," AIAA Journal , Vol. 9, 1971, pp. 2062-2063.