Simon Wang

Free vibration analysis of skew fibre-reinforced composite laminates based on first-order shear deformation plate theory

Abstract Skew fibre-reinforced composite laminates are important structural elements in modern engineering structures, particularly in aero-space industry. Natural frequencies of these skew laminates are of primary significance to structural designers. As far as the authors knowledge is concerned the references on this topic is very limited. Within the context of the first-order shear deformation plate theory (SDPT) [Reissner, The effect of transverse shear deformation on the bending of elastic plates. J. Appl. Mech. ASME , 12 , 69–76 (1945); Mindlin, influence of rotary inertia and shear on flexural motions of isotropic elastic plates. J. Appl. Mech. ASME , 12 (18), 1031–1036 (1951).] this paper presents a B-spline Rayleigh-Ritz method (RRM) for free vibration analysis of skew fibre-reinforced composite laminates which may have arbitrary lay-ups, admitting the possibility of coupling between in-plane and out-of-plane behaviour and general anisotropy. In this approach the displacement field consists of the three mid-surface translational displacements u , v and w and the two through-thickness shear strains γ xz and γ yz instead of the two rotations ψ x and ψ y in order to avoid the shear locking phenomenon. Various numerical applications are presented and the method is shown to be accurate and efficient.

Nonlinear transient analysis of rectangular composite laminated plates

The semi-analytical finite strip method is developed for the analysis of the geometrically nonlinear response to dynamic loading of rectangular composite laminated plates. The plates have simply supported ends and their properties are evaluated in the context of first-order shear deformation plate theory. The applied loading acts normal to the plate surface but otherwise may be of a general nature with respect to space and time. Solution to the nonlinear dynamic problem is obtained through use of the Newmark time-stepping scheme in association with Newton–Raphson iteration. Applications are described which relate to isotropic and orthotropic plates, and to laminates. In general a close comparison is demonstrated between the predictions of the developed finite strip approach and those of a finite element method.

Spline finite strip analysis of the buckling and vibration of rectangular composite laminated plates

Abstract A spline finite strip capability is presented for predicting the buckling stresses and natural frequencies of rectangular laminated plates. The plates may have arbitrary lay-ups and general boundary conditions. The spline finite strip method is first developed in the context of first-order shear deformation plate theory and then, by reduction, the method is also developed in the context of classical plate theory. In both approaches the superstrip concept is incorporated into the solution procedure. A considerable range of types of application is described and it is demonstrated that the spline finite strip method is versatile, with good convergence characteristics and accuracy. In these applications, frequent comparison is made with the results of other approaches which comprise a spline Rayleigh-Ritz method, a finite element method, an analytical Rayleigh-Ritz method and a semi-analytical finite strip method.

Dynamic instability of composite laminated rectangular plates and prismatic plate structures

Abstract Periodic dynamic loadings may cause dynamic instability of a structure through parametric resonance. In this paper, a B-spline finite strip method (FSM) is presented for the dynamic instability analysis of composite laminated rectangular plates and prismatic plate structures, based on the use of first-order shear deformation plate theory (SDPT). The equations of motion of a structure are established by using Lagranges formulation and they are a set of coupled Mathieu equations. The boundary parametric resonance frequencies of the motion are determined by using the method suggested by Bolotin through a novel development which incorporates the Sturm sequence method and the multi-level substructuring technique to achieve reliability, efficiency and accuracy. Various loading patterns, arbitrary lamination and general boundary conditions are accommodated. A variety of numerical applications is presented to test the developed method and to study the dynamic instability behaviour of single plates and of complicated plate structures under various types of dynamic loading. A dynamic instability index (DII) is devised to measure the degree of instability against certain parameters which include the thickness-to-length ratio, the degree of orthotropy, the fibre orientation, the loading pattern and the boundary conditions.

A UNIFIED TIMOSHENKO BEAM B-SPLINE RAYLEIGH–RITZ METHOD FOR VIBRATION AND BUCKLING ANALYSIS OF THICK AND THIN BEAMS AND PLATES

First, the shear-locking phenomenon in the wψBkSRRM1–3 is investigated and the shear-locking terms are identified in both one-dimensional beam and two-dimensional plate analyses. Subsequently the shear-locking free conditions are proposed and under the guidance of these conditions the Timoshenko beam B-spline Rayleigh–Ritz method, designated as TBkSRRM, is formulated for vibration analysis of beams based on Timoshenko beam theory and vibration and buckling analysis of isotropic plates or fibre-reinforced composite laminates based on the first-order shear deformation plate theory (SDPT). In TBkSRRM the number of degrees of freedom is exactly the same as that when the Bernoulli–Euler beam theory or classical plate theory (CPT) is used. However, the TBkSRRM includes the through-thickness shearing and rotary inertia effects in full. Several numerical applications are presented and they show that this unified approach is extremely efficient for both thick and thin beams and plates.

Buckling analysis of skew fibre-reinforced composite laminates based on first-order shear deformation plate theory

Abstract This paper presents a B-spline Rayleigh-Ritz method (RRM) based on first-order shear deformation plate theory 1,2 (SDPT) for buckling analysis of skew fibre-reinforced composite laminates which are important structural elements in modern engineering structures, particularly in the aerospace industry. The laminates considered may have arbitrary lay-ups, admitting the possibility of coupling between in-plane and out-of-plane behaviour and general anisotropy. Various numerical applications are conducted and the method is proved to be accurate and efficient. It is observed that the effect of through-thickness shear deformation is very large for moderately thick skew laminates and increases with the increase of skew angles. The analysis based on the classical plate theory (CPT) could grossly overestimate critical buckling stresses. As far as the authors knowledge is concerned it seems that there is no paper in the open literature, up to now, dealing with the buckling problems of skew fibre-reinforced composite laminates based on SDPT. Therefore, all the present results are presented in a manner of full convergence studies and it is hoped that they could be useful for designers and researchers who may use them as benchmark values to test the validity and convergence of their numerical techniques and software for similar problems.

Spline finite strip analysis of the buckling and vibration of composite prismatic plate structures

Abstract A spline finite strip capability is described for predicting the buckling stresses and natural frequencies of vibration of prismatic plate structures which may be of composite laminated construction with arbitrary lay-ups. The plate structures may have general boundary conditions. The capability embraces analyses based on the use of first-order shear deformation plate theory and of classical plate theory, and utilizes substructuring procedures which include the use of superstrips. The theoretical development is not detailed since the present paper reports a very direct extension of a theoretical study developed for the analysis of single plates in an earlier paper in this Journal. A considerable range of buckling and vibration applications is documented and comparison of spline finite strip numerical values of buckling stresses and frequencies is made with results generated using the semi-analytical finite strip method and, in some cases, the finite element method. Buckled and vibrational mode shapes are presented for some applications.

Finite strip large deflection and post-overall-buckling analysis of diaphragm-supported plate structures

A semi-analytical finite strip method is described for the analysis of the overall, geometrically non-linear, elastic behaviour of diaphragm-supported prismatic plate structures which may be made of composite laminated material and may have initial geometric imperfections. Both the large-deflection problem and the post-overall-buckling (under progressive end shortening) problem are considered. Enhanced strain-displacement relationships are used in the development of the properties of a range of finite strip models, and particular attention is paid to the appropriate representation of the longitudinal displacement. The development is made in the contexts of both first-order shear deformation and classical plate theories. A description is given of a small number of applications, most of which concern blade-stiffened panels. A comparison is made between the predictions of the developed finite strip method and those of a commercial finite element package, and such comparison is shown to be close.

Spline FSM postbuckling analysis of shear-deformable rectangular laminates

A spline finite strip method is developed for the prediction of the geometrically non-linear response of rectangular, composite laminated plates to progressive in-plane loading. The development takes place within the context of the use of the first-order shear deformation plate theory and the non-linearity is introduced in the strain-displacement equations in the manner of the von Karman assumption. A number of applications of the new capability is described, involving laminates subjected to progressive uniform end shortening and to progressive in-plane shearing. In all the applications a close comparison of the finite strip results with independent finite element results is demonstrated.

Buckling of composite shell structures using the spline finite strip method

The development of an analysis capability for predicting the buckling stresses of composite laminated, prismatic shell structures is described. The basis of the capability is the spline finite strip method, which is presented in the contexts of both first-order shear deformation shell theory and thin shell theory. The structures considered might have arbitrary lamination and general boundary conditions, and the applied stress field in any component flat or curved plate may include shear stress as well as biaxial direct stresses. Multi-level substructuring procedures are used in an efficient solution procedure. The analysis capability is incorporated into a computer software package called PASSAS and selected applications using this package are presented to show the scope and power of the new capability.