Geometric nonlinear analysis of stiffened plates by the spline finite strip method

Geometric nonlinear analysis of stiffened plates is investigated by the spline finite strip method. von Karman’s nonlinear plate theory is adopted and the formulation is made in total Lagrangian coordinate system. The resulting nonlinear equations are solved by the Newton–Raphson iteration technique. To analyse plates having any arbitrary shapes, the whole plate is mapped into a square domain. The mapped domain is discretised into a number of strips. In this method, the displacement interpolation functions used are: the spline functions in the longitudinal direction of the strip and the finite element shape functions in the other direction. The stiffener is elegantly modelled so that it can be placed anywhere within the plate strip. The arbitrary orientation of the stiffener and its eccentricity are incorporated in the formulation. All these aspects have ultimately made the proposed approach a most versatile tool of analysis. Plates and stiffened plates are analysed and the results are presented along with those of other investigators for necessary comparison and discussion.     

Analysis of piezolaminated plates by the spline finite strip method

This paper deals with the development of a family of higher order B-spline finite strip models applied to the static and free vibration analysis of laminated plates, with arbitrary shape and lay-ups, loading and boundary conditions. The lamination scheme can be such that the embedded and/or surface bonded piezoelectric actuating and sensing layers are included. The structure is discretised in a specified number of strips, and the geometry and displacement components of each strip are represented by interpolating functions that are products of linear or cubic B-spline, and linear or quadratic Lagrange functions along the y and x orthonormal directions. The accuracy and relative performance of the proposed discrete models are compared and discussed among the developed and alternative models.     

Stability analysis of skew orthotropic plates by the finite strip method

A stability analysis based on the Finite Strip Method is presented for skew orthotropic plates subjected to in-plane loadings. The straight sides of the plate are simply supported and the other two skewed sides are supported with any combination of fixed, free and simply supported boundaries. The plate is divided into strips, in contradistinction to elements in the Finite Element Method, and the displacement function is so chosen that it satisfies the boundary conditions and also the inter-strip compatibility conditions of an elemental strip. The energy expressions required to formulate the stiffness and stability coefficient matrices are formulated using smalldeflection theory. The buckling load intensity factor is evaluated for different aspect ratios of isotropic and orthotropic skew plates and the results of certain rectangular isotropic cases are compared with earlier investigations.     

Vibration analysis of rectangular mindlin plates by the finite strip method

A finite strip analysis of the vibration of rectangular Mindlin plates with general boundary conditions is described. The normal modes of vibration of Timoshenko beams are used to represent the spatial variation along a strip of the deflection and the two cross-sectional rotations. For the crosswise representation equal-order polynomial interpolation is employed for each of these three basic quantities. The accuracy of the approach is demonstrated by the results of a number of applications to square plates with combinations of simply supported, clamped and free edges.     

Bending analysis of rectangular moderately thick plates using spline finite element method

A bending analysis of rectangular, moderately thick plates with general boundary conditions is presented using the spline element method. The cubic B spline interpolate functions are used to construct the field function of generalized displacements w, φ_itxand φ_ity. The spline finite element equations are derived based on the potential energy principle. For simplicity, the boundary conditions, which consist of three local spline points, are amended to fit specified boundary conditions. The shear effect is considered in the formulations. A number of numerical examples are described for rectangular, moderately thick plates. Since the cubic B spline interpolate functions have sufficient continuity and are piecewise polynomial, so the present numerical solutions show not only that the method gives accurate results, but also that the unified solutions of thick and thin plates can be directly obtained; the trouble with the so-called shear locking phenomenon does not occur here.     

Geometrically nonlinear analysis of rectangular mindlin plates using the finite strip method

A general finite strip method of analysis is presented for the geometrically nonlinear analysis of laterally loaded, rectangular, isotropic plates. The analysis is based on the use of Mindlin plate theory and therefore includes the effects of transverse shear deformation. The nonlinearity is introduced via the strain-displacement equations and correspondingly the analysis pertains to problems involving moderate displacements but small rotations. The principle of minimum potential energy is used in the development of the strip and the complete plate stiffness equations and the latter equations are solved using the Newton-Raphson method. In numerical applications a particular type of finite strip is used in which all five reference quantities (three displacements and two rotations) are represented by cubic polynomial interpolation across the strip whilst the ends of the strip are simply supported for bending/shearing behaviour and immovable for membrane behaviour. These applications are concerned with uniformly loaded plates of both thin and moderately-thick geometry and detailed presentation is given of both displacement- and force-type quantities.     

Stability analysis of anisotropic laminated composite plates by finite strip method

The finite strip method has been applied to the stability analysis of rectangular shear-deformable composite laminates. However, for the plates with two opposite simply supported sides, the existing analysis was restricted to the symmetrical cross-ply laminates under compression loading.In the present study, by selecting proper displacement functions and including the coupling between different series terms, the finite strip method is extended to the stability analysis of any anisotropic laminated plates under arbitrary in-plane loading. Furthermore, a number of numerical results are presented to show the effects of thickness, fibre orientation and stacking sequence on the buckling loads.     

Analysis of plates by finite strip method

New finite strips are developed for the analysis of plates. Based on Reissner's plate theory, the effect of shear deformation is included in the formulation. To eliminate artificial hardening, the shape functions for the strips are so chosen that there is no mismatched term along the interpolation functions for the interpolation parameters. Numerical examples are reported to demonstrate that the strips can work equally well in thick as well as thin plates.     

Refined three-dimensional finite strip model for analysis of thick composite sandwich plates

A refined three-dimensional finite strip model for stress analysis of thick hybrid composite sandwich plates is presented in the present article. The new model is based on a combination of two different strip elements: quadratic linear skin strip (QLSS), and modified quadratic cubic core strip (MQCCS). The applications of the proposed model for sandwich plates containing a local damage under membrane or bending loading are illustrated. Numerical results are compared to independent solutions and measured data and found to be in excellent agreement. A comprehensive discussion of the numerical aspects of the method is conducted to test the strips' characteristics regarding the spectral accuracy, finite element convergence and accuracy of numerical integrations.     

Thermal post-buckling analysis of imperfect shear-deformable plates on two-parameter elastic foundations

A thermal post-buckling analysis is presented for a shear-deformable rectangular plate subjected to uniform or non-uniform tent-like temperature loading and resting on a two-parameter elastic foundation. The initial goemetrical imperfection of the plate is taken into account. The formulations are based on the Reissner-Mindlin plate theory considering the first order shear deformation effect and including thermal effects. The analysis uses a deflection-type perturbation technique to determine the thermal buckling loads and post-buckling equilibrium paths. Numerical examples cover the performances of perfect and imperfect, shear-deformable plates resting on Winkler or Pasternak-type elastic foundations.     

Buckling of initially stressed mindlin plates using a finite strip method

The buckling of initially stressed Mindlin plates is considered using a thick finite strip method. The method is compared with a wide variety of published results and for both thin and moderately thick plates excellent accuracy is obtained. Some further results are obtained for initially stressed rectangular plates with two opposite edges simply supported and various support conditions on the remaining sides. In general, it is found that for moderately thick plates, Mindlin's plate theory gives lower buckling loads than those obtained using classical thin plate theory.     

Stability analysis for plates using the multivariable spline element method

The multivariable spline element method is used in this paper to solve the stability problems of plates and beams. The bicubic spline functions are employed to construct the bending moments, twisting moments and transverse displacements field. The spine eigenvalue equations with multiple variables are derived based on the Hellinger-Reissner mixed variational principle. Some numerical examples are given, the results are good agreement with other methods.     

Three-dimensional finite strip analysis of laminated panels

In this paper, a combined finite strip and state space approach is introduced to obtain three-dimensional solutions of laminated composite plates with simply supported ends. The finite strip method is used to present in-plane displacement and stress components, while the through-thickness components are obtained by using the method of state equation. The method can replace the traditional three-dimensional finite element solutions for structures that have regular geometric plans and simple boundary conditions, where a full three-dimensional finite element analysis is very often both extravagant and unnecessary. The new method provides results that show good agreement with available benchmark problems having different material compositions, thickness and boundary conditions. The new method provides a three-dimensional solution for laminated plates, while the advantages of using the traditional finite strip method are fully taken. This solution also yields a continuous transverse stress field across material interfaces that normally is not achievable by other numerical modelling of laminates, such as the traditional finite element method.     

Three-dimensional finite strip analysis of elastic solids

Three-dimensional finite strips are formulated by combining finite element shape functions with beam eigenfunctions. Because of the orthogonality of the beam functions, three-dimensional problems are reduced to a series of two-dimensional ones whose stiffness matrices often have a very narrow bandwidth, thus significantly reducing the computational effort and storage requirements of three-dimensional analyses. Isoparametric and high order quadrilateral three-dimensional (3-D) finite strips along with illustrative examples are presented. Results are compared with existing solutions and experimental data. Good agreements are obtained in all cases.     

A simple method for the inclusion of external and internal supports in the spline finite strip method (SFSM) of buckling analysis

The SFSM is an attractive numerical technique for the buckling analysis of folded-plate structures where general loading regimes and boundary conditions need to be modelled. In implementing splines as interpolation functions in the longitudinal direction of the strip, amended splines have been used conventionally to model the variety of end conditions that may occur. These amended splines are fairly difficult to implement, particularly so if internal restraints are also to be specified. A simple technique for replacing the specification of dedicated amended splines is presented in this paper. The method is then employed to study the local buckling of flat plates under longitudinally and transversely varying compression and bending with different boundary conditions at the ends.     

Elastic-viscoplastic analysis of plates by the finite element method

In this paper the finite element technique is employed in the solution of elastic-viscoplastic plate bending problems. The method is applicable to both thick and thin plates and by attaining steady-state conditions the process offers an alternative method of solution for static elasto-plastic situations. A quadratic isoparametric element based on Mindlin plate theory is adopted and the Euler time-stepping scheme is employed in solution. Yield criteria are based on moment resultants and the Von Mises, Tresca and Johansen forms are included. Several numerical examples are presented and the results compared with those from other sources where available     

Three-dimensional finite element analysis of thick laminated plates

A displacement-based, three-dimensional finite element scheme is proposed for analyzing thick laminated plates. In the present formulation, a thick laminated plate is treated as a three-dimensional inhomogeneous anisotropic elastic body. Particular attention is focused on the prediction of transverse shear stresses. The plane of a laminated plate is first discretized into conventional eight-node elements. Various through-thickness interpolation is then denned for different regions of the plate; layerwise local shape functions are used in the regions where transverse shear stresses are of interest, while an ad hoc global-local interpolation is used in the region where only the general deformation pattern is concerned. For satisfying the displacement compatibility between these two regions, a transition zone is introduced. The model incorporates the advantages of the layerwise plate theory and the single-layer plate theory. Details of formulation will be presented together with several numerical examples for demonstrating the proposed scheme.     

Nonlinear analysis of skew plates using the finite element method

In this paper finite element analysis of the large deflection behaviour of skew plates has been done. A high precision conforming triangular plate bending element has been used. The central deflection, bending and membrane stresses have been reported for simply supported and clamped rhombic plates. The variations of these quantities have been studied for different skew angles.     

Higher order finite strip analysis for curved bridge decks

The development of a higher order finite strip method for improved accuracy and its application to orthotropic curved bridge decks are discussed. A quintic polynomial in the radial direction is employed along with a basic function series in the angular direction which satisfy a priori the boundary conditions along the radial edges. Thus a two-dimensional plate bending problem is reduced to a one-dimensional one. As a result, both the size and bandwidth of the global stiffness matrix are greatly reduced. The method is easy to program, requires a minimum input data and small computer storage. In order to estimate the reliability of the present formulation, three examples of curved plates are solved and the results are compared with the existing solutions.