Publications on Plates, Shells, Beams and Rods

Plates

1. A.J.M. Ferreira, G.E. Fasshauer, R.C. Batra and J.D. Rodrigues, Static Deformations and Vibration Analysis of Composite and Sandwich Plates Using a LayerwiseTheory and RBF-PS Discretizations with Optimal Shape Parameter, Composite Structures, 86, 328-343, 2008.
2. A. J. M. Ferreira, G. E. Fasshauer, R. C. Batra, Natural Frequencies of Thick Plates Made of Orthotropic, Monoclinic, and Hexagonal Materials by a Meshless Method, J. of Sound and Vibration, 319, 984-992, 2009.
3. R. C. Batra, M. Porfiri and D. Spinello, Reduced-order Models for Microelectromechanical Rectangular and Circular Plates Incorporating the Casimir Force, Int. J. Solids and Structures, 45, 3558-3583, 2008.
4. R. C. Batra, M. Porfiri and D. Spinello, Effects of van derWaals Force and Thermal Stresses on Pull-in Instability of Clamped Rectangular Microplates, Sensors, 8, 1048-1069, 2008.
5. R. C. Batra, M. Porfiri, and D. Spinello, Vibrations and Pull-in Instabilities of Microelectromechanical von Karman Elliptic Plates Incorporating the Casimir Force, J. of Sound and Vibration, 315, 939-960, 2008.
6. R. C. Batra, Higher Order Shear and Normal Deformable Theory for Functionally Graded Incompressible Linear Elastic Plates, Thin-Walled Structures, 45, 974-982, 2007.
7. M. C. Ray and R. C. Batra, Vertically Reinforced 1-3 Piezoelectric Composites for Active Damping of Functionally Graded Plates, AIAA J. 45:7, 1779-1783, 2007.
8. R. C. Batra and S. Romano, Failure of Dynamically Loaded Thermoelastoviscoplastic Rectangular Plate, AIAA J. 45:8, 2015-2023, 2007.
9. R. C. Batra and S. Aimmanee, Vibration of an Incompressible Isotropic Linear Elasatic Rectangular Plates with a Higher Order Shear and Normal Deformable Theory, J. of Sound and Vibration, 307, 961-971, 2007.
10. J. R. Xiao, D. F. Gilhooley, R. C. Batra, J. W. Gillespie Jr. and M. A. McCarthy, Analysis of Thick Composite Laminates Using a Higher-Order Shear and Normal Deformable Plate Theory (HOSNDPT) and a Meshless Method, Composites B, 39, 414-427, 2008.
11. A. Ferreira, C. Roque, G. Fasshauer, R. Jorge and R. Batra, Analysis of Functionally Graded Plates by a Robust Meshless Method, Mechanics of Advanced Materials and Structures, 14, 577-587, 2007.
12. S. Aimmanee and R. C. Batra, Analytical Solution for Vibration of an Incompressible Isotropic Linear Elastic Rectangular Plate, and Frequencies Missed in Previous Solutions, J. Sound and Vibration, 302, 613-620, 2007.
13. J. R. Xiao, R. C. Batra, D. F. Gilhooley, J. W. Gillespie, Jr. and M. A. McCarthy, Analysis of Thick Plates by using a Higher-Order Shear and Normal Deformable Plate Theory and MLPG Method with Radial Basis Functions, Computer Methods in Applied Mechanics and Engineering, 196, 979-987, 2007.
14. D. F. Gilhooley, R. C. Batra, J. R. Xiao, M. A. McCarthy, J. W. Gillespie Jr., Analysis of Thick Functionally Graded Plates by using Higher-Order Shear and Normal Deformable Plate Theory and MLPG Method with Radial Basis Functions, Composite Structures, 80, 539-552, 2007.
15. A.J.M. Ferreira, R.C. Batra, C.M.C. Roque, L.F. Qian, R.M.N. Jorge, Natural Frequencies of Functionally Graded Plates by a Meshless Method, Composite Structures,75, 593-600, 2006.
16. S. R. Li, R. C. Batra and L.-S. Ma, Vibration of Thermally Post-Buckled Orthotropic Circular Plates, J. Thermal Stresses, 30, 43-57, 2007.
17. R. C. Batra and Zhicun Wang, Failure Mode Transition Speed in Three-Dimensional Transient Deformations of a Microporous Heat-ConductingThermoelastoviscoplastic Prenotched Plate, J. Thermal Stresses, 28, 533-562, 2005.
18. R. C. Batra and S. Aimmanee, Vibrations of Thick Isotropic Plates with Higher Order Shear and Normal Deformable Plate Theories, Computers & Structures, 83, 934-955, 2005.
19. A. Ferreira and R. C. Batra, Natural Frequencies of Orthotropic, Monoclinic and Hexagonal Plates by a Meshless Method, J. of Sound and Vibration, 285, 734-742, 2005.
20. R. C. Batra, Z. G. Wei, Dynamic Buckling of a Thin Thermoviscoplastic Rectangular Plate, Thin-Walled Structures, 43, 273-290, 2005.
21. L. F. Qian and R. C. Batra, Three-Dimensional Transient Heat Conduction in a Functionally Graded Thick Plate with a Higher-Order Plate Theory and a Meshless LocalPetrov-Galerkin Method, Computational Mechanics , 35, 214-226, 2005.
22. A. J. M. Ferreira, R. C. Batra, C. M. C. Roque, L. F. Qian and P. A. L. S. Martins, Static Analysis of Functionally Graded Plates Using Third-order Shear Deformation Theory and a Meshless Method, Composite Structures, 69, 449-457, 2005.
23. R. C. Batra and J. Jin, Natural Frequencies of a Functionally Graded Anisotropic Rectangular Plate, J. Sound and Vibration, 282, 509-516, 2005.
24. R. C. Batra and M. H. Lear, Simulation of Brittle and Ductile Fracture in an Impact Loaded Prenotched Plate, Int. J. of Fracutre, 126, 179-203, 2004.
25. L. F. Qian and R. C. Batra, Transient Thermoelastic Deformations of a Thick Functionally Graded Plate, J. of Thermal Stresses, 27, 705-740, 2004.
26. L. F. Qian and R. C. Batra, Design of Bidirectional Functionally Graded Plate for Optimal Natural Frequencies, J. of Sound and Vibration, 280, 415-424, 2005.
27. L. F. Qian, R. C. Batra and L. M. Chen, Analysis of Cylindrical Bending Thermoelastic Deformations of Functionally Graded Plates by a Meshless Local Petrov-GalerkinMethod, Computational Mechanics, 33, 263-273, 2004.
28. L. F. Qian, R. C. Batra and L. M. Chen, Static and Dynamic Deformations of Thick Functionally Graded Elastic Plate by using Higher-Order Shear and Normal Deformable Plate Theory and Meshless Local Petrov-Galerkin Method, Composites: Part B, 35, 685-697, 2004.
29. S. S. Vel, R. Mewer and R. C. Batra, Analytical Solution for the Cylindrical Bending Vibration of Piezoelectric Composite Plates, Int. J. Solids & Structures, 41, 1625-1643, 2004.
30. R. C. Batra, L. F. Qian and L. M. Chen, Natural Frequencies of Thick Square Plates Made of Orthotropic, Trigonal, Monoclinic, Hexagonal and Triclinic Materials, J. Sound and Vibration, 270, 1074-1086, 2004.
31. L. F. Qian, R. C. Batra and L. M. Chen, Free and Forced Vibrations of Thick Rectangular Plates by using Higher-Order Shear and Normal Deformable Plate Theory andMeshless Petrov-Galerkin (MLPG) Method, Computer Modeling in Engineering and Sciences, 4, 519-534, 2003.
32. S. S. Vel and R. C. Batra, Three-dimensional Exact Solution for the Vibration of Functionally Graded Rectangular Plates, J. of Sound and Vibration 272, 703-730. 2004.
33. S. S. Vel and R. C. Batra, Three-dimensional Analysis of Transient Thermal Stresses in Functionally Graded Plates, Int. J. of Solids & Structures, 40, pp. 7181-7196, 2003.
34. R. C. Batra and S. Aimmanee, Missing Frequencies in Previous Exact Solutions of Free Vibrations of Simply Supported Rectangular Plates, J. of Sound & Vibrations,265, 887-896, 2003.
35. L. F. Qian, R. C. Batra and L. M. Chen, Elastostatic Deformations of a Thick Plate by using a Higher-Order Shear and Normal Deformable Plate Theory and TwoMeshless Local Petrov-Galerkin (MLPG) Methods, Computer Modeling in Eng'g and Sciences, 4, 161-176, 2003.
36. S. S. Vel and R. C. Batra, Generalized Plane Strain Thermopiezoelectric Analysis of Multilayered Plates, J. Thermal Stresses, 26, 353-377, 2003.
37. R. C. Batra, S. Vidoli and F. Vestroni, Plane Waves and Modal Analysis in Higher-Order Shear and Normal Deformable Plate Theories, J. Sound & Vibration, 257(1), 63-88, 2002.
38. S. S. Vel and R. C. Batra, Exact Solutions for Thermoelastic Deformations of Functionally Graded Thick Rectangular Plates, AIAA J., 40(7), 1421-1433, 2002.
39. R. C. Batra and T. S. Geng, Enhancement of the Dynamic Buckling Load for a Plate by Using Piezoceramic Actuators, Smart Materials & Structures, 10, 925-933, 2001.
40. R. C. Batra, N. A. Jaber and M. E. Malsbury, Analysis of Failure Modes in an Impact Loaded Thermoviscoplastic Prenotched Plate, Int. J. Plasticity, 19(2), 139-196, 2003.
41. R. C. Batra and S. Vidoli, Higher Order Piezoelectric Plate Theory Derived from a Three-Dimensional Variational Principle, AIAA J., 40(1), 91-104, 2002.
42. S. S. Vel and R. C. Batra, Exact Solution for Rectangular Sandwich Plates with Embedded Piezoelectric Shear Actuators, AIAA J., 39, 1363-1373, 2001.
43. R. C. Batra and N. A. Jaber, Failure Mode Transition Speeds in an Impact Loaded Prenotched Plate with Four Thermoviscoplastic Relations, Int. J. Fracture, 110, 47-71, 2001.
44. S. S. Vel and R. C. Batra, Exact Solution for the Cylindrical Bending of Laminated Plates with Embedded Shear Actuators, Smart Materials & Structures, 10, 240-251, 2001.
45. S. S. Vel and R. C. Batra, Analysis of Piezoelectric Bimorphs and Plates with Segmented Actuators, Thin-Walled Structures, 39(1), 23-44, 2001.
46. S. S. Vel and R. C. Batra, Generalized Plane Strain Thermoelastic Deformation of Laminated Anisotropic Thick Plates, Int. J. Solids Structures, 38, 1395-1414, 2001.
47. S. Vidoli and R. C. Batra, Derivation of Plate and Rod Equations for a Piezoelectric Body from a Mixed Three-Dimensional Variational Principle, J. Elasticity, 59, 23-50, 2000.
48. S. S. Vel and R. C. Batra, Three-dimensional Analytical Solutions for Hybrid Multilayered Piezoelectric Plates,  J. Appl. Mechs., 67, 558-567, 2000.
49. S. S. Vel and R. C. Batra, Closure to The Generalized Plane Strain Deformations of thick Anisotropic Composite Laminated Plates, Int. J. Solids Structures, 38, 483-489, 2000.
50. Z.-Q. Cheng and R. C. Batra, Deflection Relationships Between the Homogeneous Plate Theory and Different Functionally Graded Plate Theories, Archives of Mechanics, 52, 143-158, 2000.
51. Z.-Q. Cheng and R. C. Batra, Three-Dimensional Thermoelastic Deformations of a Functionally Graded Elliptic Plate, Composites B, 31, 97-106, 2000.
52. S. S. Vel and R. C. Batra, Cylindrical Bending of Laminated Plates with Distributed and Segmented Piezoelectric Actuator/Sensors, AIAA J., 38, 857-867, 2000.
53. R. C. Batra and R. R. Gummalla, Effect of Material and Geometric Parameters on Deformations Near the Notch-tip of a Dynamically Loaded Prenotched Plate, Int. J. Fracture, 101, 99-140, 2000.
54. Z. Q. Cheng and R. C. Batra, Exact Correspondence Between Eigenvalues of Membranes and Functionally Graded Simply Supported Polygonal Plates, J. Sound & Vibration, 229, 879-895, 2000.
55. S. S. Vel and R. C. Batra, The Generalized Plane Strain Deformations of Thick Anisotropic Composite Laminated Plates, Int. J. Solids Structures, 37, 715-733, 2000.
56. S. Vel and R. C. Batra, Analytical Solutions for Rectangular Thick Laminated Plates Subjected to Arbitrary Boundary Conditions, AIAA J., 37, 1464-1473, 1999.
57. N. V. Nechitailo and R. C. Batra, Penetration/Perforation of Aluminum, Steel and Tungsten Plates by Ceramic Rods, Computers & Structures, 66, 571-583, 1998.
58. S. Krishnaswamy, Z. H. Jin and R. C. Batra, Stress Concentration in an Elastic Cosserat Plate Undergoing Extensional Deformations, J. Appl. Mechs., 65, 66-70, 1998.
59. X. Q. Liang and R. C. Batra, Changes in Frequencies of a Laminated Plate Caused by Embedded Piezoelectric Layers, AIAA J., 35, 1672-1673, 1997.
60. Z. H. Jin and R. C. Batra, A Crack at the Interface Between a Kane-Mindlin Plate and a Rigid Substrate, Eng'g Fracture Mechs., 57, 343-354, 1997.
61. Z. H. Jin and R. C. Batra, Dynamic Fracture of a Kane-Mindlin Plate, Theoretical and Applied Fracture Mechs., 26, 199-210, 1997.
62. R. C. Batra and N. V. Nechitailo, Analysis of Failure Modes in Impulsively Loaded Pre-Notched Steel Plates, Int. J. Plasticity, 13, 291-308, 1997.
63. R. C. Batra and X. Q. Liang, The Vibration of a Rectangular Laminated Elastic Plate with Embedded Piezoelectric Sensors and Actuators, Computers & Structures, 63, 203-216, 1997.
64. J. D. Wang, R. C. Batra and K. Isogimi, Analysis of Stress Distribution in a Thin Rectangular Plate by the Method of Caustics, Arch. Mechs., 48, 1011-1024, 1996.
65. R. C. Batra and Z. Peng, Development of Shear Bands during the Perforation of a Steel Plate, Computational Mechs., 17, 326-334, 1996.
66. R. C. Batra, X. Q. Liang and J. S. Yang, The Vibration of a Simply Supported Rectangular Elastic Plate due to Piezoelectric Actuators, Int. J. Solids \& Structures, 33, 1597-1618, 1996.
67. R. C. Batra, X. Q. Liang and J. S. Yang, Shape Control of Vibrating Simply Supported Plates, AIAA J., 34, 116-122, 1996.
68. R. C. Batra and K. Ghosh, Deflection Control During Dynamic Deformations of a Rectangular Plate Using Piezoceramic Elements, AIAA J., 33, 1547-1548, 1995.
69. K. Ghosh and R. C. Batra, Shape Control of Plates Using Piezoceramic Elements, AIAA J., 33, 1354-1357, 1995.
70. J. S. Yang, R. C. Batra and X. Q. Liang, The Cylindrical Bending Vibrations of a Laminated Elastic Plate Due to Piezoelectric Actuators, Smart Materials & Strucutres,3, 485-493, 1994.
71. J. S. Yang and R. C. Batra, A Theory of Electroded Thin Thermopiezoelectric Plates Subject to Large Driving Voltages, J. Appl. Physics, 76, 5411-5417, 1994.
72. A. Kadic-Galeb and R. C. Batra, Stress Distribution in an Elastic Perfectly Plastic Plate Subjected to Corrosive Environmental Loads, Int. J. Engng Sci., 31, 1301 - 1307, 1993.
73. R. C. Batra and R. N. Dubey, Impulsive Loading of Circular Plates, Int. J. Solids and Structures, 7, 965-978, 1971.

Shells

74. M. C. Ray and R. C. Batra, Smart Constrained Layer Damping of Functionally Graded Shells using Vertically/Obliquely Reinforced 1-3 Piezocomposite under Thermal Environment, Smart Materials and Structures, 17, 055007 (13pp), 2008.
75. S.-R. Li and R. C. Batra, Buckling of Axially Compressed Cylindrical Shells with Functionally Graded Middle Layer, Thin-Walled Structures, 44, 1039-1047, 2006.
76. Z. G. Wei and R. C. Batra, Dynamic Buckling of Thin Thermoviscoplastic Cylindrical Shell under Radial Impulsive Loadnig, Thin-Walled Structures, 44, 1109-1117, 2006.
77. Z. G. Wei, J. L. Yu and R. C. Batra, Dynamic Buckling of Thin Cylindrical Shells under Axial Impact, Int. J. Impact Engng., 32, 575-592, 2005.
78. Z.-Q. Cheng and R. C. Batra, Thermal Effects on Laminated Composite Shells Containing Interfacial Imperfections, J. Comp. Structures, 52(1), 3-11, 2001.
79. J. S. Yang and R. C. Batra, Thickness Shear Vibrations of a Circular Cylindrical Piezoelectric Shell, J. Acoustic Soc. America, 97, 309- 312, 1995.

Rods

80. S. Vidoli and R. C. Batra, Derivation of Plate and Rod Equations for a Piezoelectric Body from a Mixed Three-Dimensional Variational Principle, J. Elasticity, 59, 23-50, 2000.
81. S. Krishnaswamy and R. C. Batra, On Extensional Vibration Modes of Elastic Rods of Finite Length which include the Effect of Lateral Deformation, {\it J. Sound & Vibration, 215, 577-586, 1998.
82. S. Krishnaswamy and R. C. Batra, Addendum to ``On Extensional Oscillations and Waves in Elastic Rods,'' Math. & Mech. Solids, 3, 297-301, 1998.
83. S. Krishnaswamy and R. C. Batra, On Extensional Oscillations and Longitudinal Waves in Elastic Rods, Math. & Mech. Solids, 3, 277-295, 1998.