A finite element large displacement analysis of stiffened plates

A finite element analysis of the large deflection behaviour of stiffened plates using the isoparametric quadratic stiffened plate bending element is presented. The evaluation of fundamental equations of the stiffened plates is based on Mindlin's hypothesis. The large deflection equations are based on von Kármán's theory. The solution algmrithm for the assembled nonlinear equilibrium equations is based on the Newton-Raphson iteration technique. Numerical solutions are presented for rectangular plates and skew stiffened plates.     

Finite element free vibration of eccentrically stiffened plates

An isoparametric stiffened plate element is introduced for the free vibration analysis of eccentrically stiffened plates. The element has the ability to accommodate irregular boundaries. Moreover, the formulation considers shear deformation, hence, the formulation is applicable to both thick and thin plates. In the present formulation, the stiffeners can be placed anywhere within the plate element and they need not necessarily follow the nodal lines. In addition, the effects of lumped and consistent mass matrices on natural frequencies of stiffened plates are investigated. The effects of several parameters of the stiffener—eccentricity, shape, torsional stiffness etc.—on the natural frequencies of the stiffened plates are studied.     

Vibration of stiffened skew plates by using B-spline functions

This paper presents a general procedure for calculating the free vibration of stiffened skew plates by the Rayleigh-Ritz method with B-spline functions as coordinate functions. The stiffened skew plates are modelled as the skew plate with a number of stiffening beams.The results are compared with existing values based on other numerical methods. Vibration characteristics of stiffened skew plates are also studied with changing the arrangements of stiffening beams, the stiffness parameters of beams, skew angle and aspect ratio.     

Natural vibrations of shear deformable cantilevered skewed trapezoidal and triangular thick plates

In a recent companion paper, the efficacy of higher-order shear deformable, C⁰ continuous, Lagrangian isoparametric plate finite element analyses has been demonstrated on cantilevered skewed (parallelogram) thick plates. The present work extends the method to include skewed thick plates having trapezoidal and triangular planforms, and is the first known vibrational study of such plates. Extensive and accurate nondimensional frequency tables and graphical charts are presented for a series of trapezoidal plates showing the effect of aspect ratio, chord ratio, thickness ratio, and skew angle. The need for the present higher-order shear deformable plate finite element method for skewed trapezoidal plate vibrations increases as the skew angle increases and as the aspect ratio, chord ratio, and thickness ratio decreases. Some theoretical and experimental data hitherto published for delta and skewed triangular cantilevered plates are compared with results obtained using the present finite element method. No published theoretical results for cantilevered skewed trapezoidal and triangular thick plates are known to exist.     

Finite element free flexural vibration analysis of plates having various shapes and varying rigidities

Natural frequencies of skew, curved and tapered plates have been determined using the isoparametric quadratic plate bending element. Plates having linearly varying thickness in one direction and also those having parabolically varying thickness in orthogonal directions have been analysed. A simple stepped plate approach for a linearly tapered plate has also been considered to compare the results. Two approaches have been adopted for the solution of skew plates. In one case, the boundary conditions have been exactly satisfied by transforming the rotational displacements at the boundary nodes along and normal to the edge. In the other case, only the vertical deflection was locked. A curved plate has also been analysed by the first method. Results thus obtained from both cases have been compared.     

铝合金受压板件局部屈曲承载力设计方法

为考察现有铝合金设计规范预测非焊接受压板件承载力的准确性,采用壳单元建立单向受压四边简支板、方形截面管柱和十字形截面轴压柱有限元模型,使用ANSYS计算得到铝合金板件弹塑性屈曲临界应力和极限承载力。数值计算结果与理论分析结果对比发现：现有板件弹塑性屈曲应力理论能够给出铝合金板件屈曲临界应力的下限值,误差较小。中国规范非加劲板件有效厚度预测公式偏保守,因此给出修正的有效厚度预测公式。修正后的非加劲板件有效厚度公式可以提高板件利用率,增强经济性。     

Compressive buckling analysis and design of stiffened flat plates with multilayered composite reinforcement

This paper describes an analysis and its application in design for compressive buckling of flat stiffened plates considered as an assemblage of linked orthotropic flat plate and beam elements. Plates can be multilayered, with possible coupling between bending and stretching. Structural lips and beads are idealized as beams. The plate and the beam elements are matched along their common junctions for displacement continuity and force equilibrium in an exact manner. Buckling loads are found as the lowest of all possible general and local failure modes. The mode shape is used to determine whether buckling is a local or general instability and is particularly useful to the designer in identifying the weak elements for redesign purposes. Typical design curves are presented for the initial buckling of a hat stiffened plate locally reinforced with boron fiber composite.     

Free vibration and buckling analyses of CNT reinforced laminated non-rectangular plates by discrete singular convolution method

This paper presents the free vibration and buckling analyses of functionally graded carbon nanotube-reinforced (FG-CNTR) laminated non-rectangular plates, i.e., quadrilateral and skew plates, using a four-nodded straight-sided transformation method. At first, the related equations of motion and buckling of quadrilateral plate have been given, and then, these equations are transformed from the irregular physical domain into a square computational domain using the geometric transformation formulation via discrete singular convolution (DSC). The discretization of these equations is obtained via two-different regularized kernel, i.e., regularized Shannon’s delta (RSD) and Lagrange-delta sequence (LDS) kernels in conjunctions with the discrete singular convolution numerical integration. Convergence and accuracy of the present DSC transformation are verified via existing literature results for different cases. Detailed numerical solutions are performed, and obtained parametric results are presented to show the effects of carbon nanotube (CNT) volume fraction, CNT distribution pattern, geometry of skew and quadrilateral plate, lamination layup, skew and corner angle, thickness-to-length ratio on the vibration, and buckling analyses of FG-CNTR-laminated composite non-rectangular plates with different boundary conditions. Some detailed results related to critical buckling and frequency of FG-CNTR non-rectangular plates have been reported which can serve as benchmark solutions for future investigations.

     

Elasto-plastic analysis of orthogonally stiffened plates with initial imperfections under uniaxial compression

In general, the stiffened plates consisting of steel plate elements are unavoidably accompanied by initial imperfections such as residual stresses and initial deflections, which have considerable effects on their ultimate strength. Therefore, it is needed for designing them to develop more rational method taking the ultimate strength influenced by initial imperfections into account rather than the conventional design method being on the basis of the linear elastic buckling theory.From this point of view, this study aims to evaluate rigorously the ultimate strength of orthogonally stiffened plate with initial imperfections under uniaxial in-plane compression. The elasto-plastic finite element method is applied to attain this purpose. By a happy combination of modal analytical technique and conventional finite element method, much reduction of the degree of freedom can be expected to be realized herewith. Some numerical calculations are performed by means of this rigorous method to examine the exactness of the analysis. Moreover, the numerical results are compared with the experimental ones.     

Isoparametric linear bending element and one-point integration

An isoparametric linear plate bending element is introduced and its use for the analysis of beams, square and rhombic plates is examined. One-point integration for the generation of an element stiffness matrix has been carried out. When compared with available solutions, the agreement of the results have been excellent. Isoparamctric linear elements have been found to be more economical than isoparametric quadratic elements at least for beams and plates with straight edges.     

Post-buckling behavior of thin steel plates using computational models

Thin plates loaded in plane will buckle at very small loads, and due to unavoidable out-of-plane imperfections, the theoretical buckling load cannot be observed experimentally. If the plate is adequately supported along its boundaries, it will be able to carry a much higher load than the theoretical buckling load.Computational models can be used to study the post buckling behaviour of thin plate structures up to failure. Failure of such structures is usually due to large out-of-plane deflections, yielding, and rupture. Therefore, the computational model should include the effects of geometric and material nonlinearities. In this paper, the nonlinear finite element analysis program NONSAP and ANSR-III were modified and used in the analysis. Since these programs did not include the suitable elements and material properties to conduct the subject study, new elements and new material properties were added to the programs. In particular, a thin shell element was added and the solution routines were modified to improve its accuracy and efficiency.The modified programs were used on a Super Computer to calculate the post buckling strength of stiffened and unstiffened plates subjected to uniaxial compression, and plates subjected to in plane bending or shear. Crippling of plates subjected to in-plane or eccentric edge compressive loads was also examined. The results from the computational models were compared with test results and reasonable agreements were obtained. A computational model was developed for a multi-story thin steel plate shear wall subjected to cyclic loading and the results from the model were compared with experimental results, and again agreement was achieved.     

Mixed elements in the optimal design of plates

The theory of design sensitivity analysis of structures, based on mixed finite element models, is developed for static, dynamic and stability constraints. The theory is applied to the optimal design of plates with minimum weight, subject to displacement, stress, natural frequencies and buckling stresses constraints. The finite element model is based on an eight node mixed isoparametric quadratic plate element, whose degrees of freedom are the transversal displacement and three moments per node. The corresponding nonlinear programming problem is solved using the commercially available ADS (Automated Design Synthesis) program. The sensitivities are calculated by analytical, semi-analytical and finite difference techniques. The advantages and disadvantages of mixed elements in design optimization of plates are discussed with reference to applications.     

Basis for isoparametric stress elements

The family of the so-called ‘isoparametric strain (displacement) elements’ is restricted to membranes and solids. The reason for this restriction has led to the development of a new family based on stress assumptions; these elements will be referred to as ‘isoparametric stress elements’. This family contains plates and solids but no membranes. The omission of a particular element in each family is consistent with the plate-membrane analogies. The basic flexibility matrix of an isoparametric stress element is singular since the zero stress state is directly included. The rank technique is adopted to automatically extract the zero stress modes such that the element can be completely interchangeable between any finite element system. The theory for stress assumed isoparametric “quadrilateral” plate bending elements with curved boundaries is given. A brief presentation of the theory for isoparametric stress solid elements is also included.     

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.     

Semi-analytical postbuckling analysis of stiffened imperfect plates with a free or stiffened edge

A large deflection, semi-analytical method is developed for pre- and postbuckling analyses of stiffened rectangular plates with one edge free or flexibly supported, and the other three edges laterally supported. The plates can have stiffeners in both directions parallel and perpendicular to the free edge, and the stiffener spacing can be arbitrary. Both global and local bending modes are captured by using a displacement field consisting of displacements representing a simply supported, stiffened plate and an unstiffened plate with a free edge. The out-of-plane and in-plane displacements are represented by trigonometric functions and linearly varying functions, defined over the entire plate. The formulations derived are implemented into a FORTRAN computer programme, and numerical results are compared with results by finite element analyses (FEA) for a variety of plate and stiffener geometries. Relatively high numerical accuracy is achieved with low computational efforts.     

Performance study of a simple finite element in the analysis of skew rhombic plates

An exhaustive study of skew rhombic plates in transverse bending is carried out using a simple three-noded element. Uniformly distributed, as well as concentrated, loads are considered for various support conditions. It is interesting to note that even for Morley's acute skew plate with singularity, very good convergence is achieved for deflection and moment values with the usual mesh pattern. Because of the inadequacy of published works, two other elements have been deployed to facilitate comparison of results. It is seen that the element under discussion fits excellently into the analysis of skew plates. Because of the availability of the element stiffness matrix in the explicit form, the use of the element is straightforward and involves less complexity. A minicomputer has been employed for the analysis and the CPU time for different elements has been reported in the convergence study for the sake of comparison.     

Stiffened plate plane stress elements for the analysis of ships' structures

A new approach has been suggested to account for the stiffeners within the plate element under plane stress. It caters accurately the spacing and orientation of the stiffeners. The derivation of the stiffeness matrix of the stiffeners placed within isoparametric and triangular elements has been presented. The advantages of the proposed approach over the conventional models have been indicated. The paper incorporates the results of a stiffened deep beam, a rectangular ship plating and a typical web frame of a tanker obtained by using these elements.     

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.     

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.     

Analysis of plates using isoparametric quadratic element—Shear,reaction, patch loading and some convergence studies

The derivation of reactions at the supported edge of a plate using isoparametric quadratic element has been presented. Straight and curved plates have been analysed to study the influence of shear rigidity, boundary conditions and support geometry on the value of shears and reactions at the edges. It has been found that convergence is slower for shear than for moments. The explicit value of the element loading matrix due to a patch load has been indicated, and plates having different aspect ratios due to a central patch load have been studied.