Mechanics of thin-walled curved beams made of composite materials, allowing for shear deformability

Abstract In this paper, a new theoretical model is developed for the generalized linear analysis of composite thin-walled curved beams with open and closed cross-sections. In the present model two important concepts concerning to composite thin-walled curved beams are addressed. The first one is the incorporation in the model of what is called full shear deformability, i.e. shear flexibility due to both bending and non-uniform warping is considered. The second feature is connected with the constitutive aspects, and it contemplates the use of different hypotheses that can be adopted in the formulation. These topics are treated in a straightforward way by means of the Linearized Principle of Virtual Work. In order to obtain the motion equations of the model a non-linear displacement field, whose rotations are formulated by means of the rule of semitangential transformation, is employed. This model allows the study of many problems of statics, free and forced vibrations with arbitrary initial stresses and linear stability of composite thin-walled curved beams with general cross-sections. A discussion about the constitutive equations is performed in order to explain characteristic features of the effects included in the theory. This paper presents the theoretical formulation together with finite element procedures that are developed to obtain the numerical approximations to the general equations of thin-walled shear-deformable composite curved beams. For this kind of structural member, iso-parametric finite elements are introduced. Numerical examples are carried out in several topics of statics, dynamics and buckling problems, focusing attention in the validation of the theory with respect to experimental data and with 2D and 3D computational approaches. Also, new parametric studies are performed in order to show the influence of shear deformability on the mechanics of the thin-walled composite curved-beams with open and closed cross-sections as well as to illustrate the utility of the model.

[1]  D. W. Scharpf,et al.  On the geometrical stiffness of a beam in space—a consistent V.W. approach , 1979 .

[2]  V. H. Cortinez,et al.  Vibration studies of composite thin-walled curved box-beam using structural tailoring , 2002 .

[3]  A. Noor,et al.  Mixed finite element models for free vibrations of thin-walled beams , 1989 .

[4]  V. Vlasov.  Thin-walled elastic beams , 1961 .

[5]  Biswajit Tripathy,et al.  Curved composite beams—optimum lay-up for buckling by ranking , 1991 .

[6]  Moon-Young Kim,et al.  Spatial free vibration of shear deformable circular curved beams with non-symmetric thin-walled sections , 2004 .

[7]  M. S. Qatu,et al.  Vibration of laminated composite arches with deep curvature and arbitrary boundaries , 1993 .

[8]  Chang-New Chen.  Dynamic equilibrium equations of composite anisotropic beams considering the effects of transverse shear deformations and structural damping , 2000 .

[9]  Alfred G. Striz,et al.  VIBRATION ANALYSIS OF HORIZONTALLY CURVED BEAMS WITH WARPING USING DQM , 1996 .

[10]  G. S. Palani,et al.  Finite Element Analysis of Thin‐Walled Curved Beams Made of Composites , 1992 .

[11]  J. Argyris.  An excursion into large rotations , 1982 .

[12]  A. Saleeb,et al.  Generalized mixed finite element model for pre- and post-quasistatic buckling response of thin-walled framed structures , 1994 .

[13]  V. Yildirim,et al.  Governing equations of initially twisted elastic space rods made of laminated composite materials , 1999 .

[14]  Víctor H. Cortínez,et al.  Mechanics of shear deformable thin-walled beams made of composite materials , 2007 .

[15]  Víctor H. Cortínez,et al.  Transverse shear deformability in the dynamics of thin-walled composite beams: consistency of different approaches , 2005 .

[16]  Y. Wang,et al.  RESPONSES OF NEAR-OPTIMAL, CONTINUOUS HORIZONTALLY CURVED BEAMS TO TRANSIT LOADS , 1999 .

[17]  K. Washizu.  Variational Methods in Elasticity and Plasticity , 1982 .

[18]  Moon-Young Kim,et al.  Spatial stability of shear deformable curved beams with non-symmetric thin-walled sections. II: F. E. solutions and parametric study , 2005 .

[19]  Nam-Il Kim,et al.  Analytical and Numerical Study on Spatial Free Vibration of Non-Symmetric Thin-Walled Curved Beams , 2002 .

[20]  A. Saleeb,et al.  Vibration Analysis of Coupled Extensional/Flexural/Torsional Modes of Curved Beams With Arbitrary Thin-Walled Sections , 1994 .

[21]  Chai H. Yoo,et al.  BUCKLING ANALYSIS OF CURVED BEAMS BY FINITE-ELEMENT DISCRETIZATION , 1996 .

[22]  Víctor H. Cortínez,et al.  DQM FOR VIBRATION ANALYSIS OF COMPOSITE THIN-WALLED CURVED BEAMS , 2001 .

[23]  R. E. Rossi,et al.  Out-of-plane vibrations of shear deformable continuous horizontally curved thin-walled beams , 2000 .

[24]  D. Hodges,et al.  Cross-sectional analysis of composite beams including large initial twist and curvature effects , 1996 .

[25]  Youngjong Kang,et al.  Free vibration analysis of horizontally curved steel I-girder bridges , 2005 .

[26]  George T. Michaltsos,et al.  EIGENFREQUENCY ANALYSIS OF THIN-WALLED GIRDERS CURVED IN PLAN , 1999 .

[27]  M. H Kadivar,et al.  Forced vibration of unsymmetric laminated composite beams under the action of moving loads , 1998 .

[28]  Moon-Young Kim,et al.  Spatial stability of shear deformable curved beams with non-symmetric thin-walled sections. I: Stability formulation and closed-form solutions , 2005 .

[29]  R. E. Rossi,et al.  Out of plane vibrations of thin-walled curved beams considering shear flexibility , 1999 .

[30]  Olivier A. Bauchau,et al.  Large displacement analysis of naturally curved and twisted composite beams , 1987 .

[31]  Víctor H. Cortínez,et al.  Stability of composite thin-walled beams with shear deformability , 2006 .