Isotropic plate elements with shear and normal strain deformations

Plate-bending finite elements are developed for thin and moderately thick plates. The element takes into account the influence of the transverse normal strain and the transverse shear effects. For the computation of the stresses, an additional plate element is developed to determine the inplane displacements and forces. The combined effects of the plate-bending and inplane elements are used for the complete solution of the problem. Several examples are solved and compared with their corresponding exact solutions.     

An approximate method for lateral stability analysis of wall-frame buildings including shear deformations of walls

This study presents an approximate method based on the continuum approach and transfer matrix method for lateral stability analysis of buildings. In this method, the whole structure is idealized as an equivalent sandwich beam which includes all deformations. The effect of shear deformations of walls has been taken into consideration and incorporated in the formulation of the governing equations. Initially the stability differential equation of this equivalent sandwich beam is presented, and then shape functions for each storey is obtained by the solution of the differential equations. By using boundary conditions and stability storey transfer matrices obtained by shape functions, system buckling load can be calculated. To verify the presented method, four numerical examples have been solved. The results of the samples demonstrate the agreement between the presented method and the other methods given in the literature.     

Instability in simple shear deformations of strain-softening materials

A quasistatic stability analysis is performed for the problem of a strain-softening material undergoing dynamic one-dimensional simple shear. This analysis is basically algebraic in nature and deals strictly with the underlying linearized problem. A simple algebraic criterion for the onset of instability is developed. An application of the criterion to two steels is then made and compared with experimental data, and qualitative agreement is observed. The analysis is then refined in a special case to include the time-dependence of the underlying parallel flow in the stability method. For a simple constitutive assumption of a thermoviscous materials), it is found that the refined analysis can yield a somewhat different stability criterion than the quasistatic analysis. The importance of this for the problem under consideration is also discussed.     

An inverse analysis method to estimate inherent deformations in thin plate welded joints

Weld-induced distortion occurs as an unavoidable consequence due to the intrinsic nature of non-uniform heating and fast cooling. Welding distortion not only negatively affects manufacturing accuracy, but also increases fabrication cost due to straightening work. Past researches suggest that elastic finite element method based on inherent strain theory is an effective approach to estimate welding deformation for welded structures. However, when this method is used to simulate welding deformation in a large or complex structure, the values of inherent deformations in each typical joint must be known beforehand. In the present study, a new method based on inverse analysis was developed to obtain the inherent deformations in typical welded joints. Meanwhile, the influence of weld length on welding deformation was investigated. In addition, using the proposed method, a database of inherent deformations in thin plate butt joints was established.     

A general methodology for deriving shear constrained Reissner-Mindlin plate elements

In this paper the necessary requirements for the good behaviour of shear constrained Reissner–Mindlin plate elements for thick and thin plate situations are re-interpreted and a simple explicit form of the substitute shear strain matrix is obtained. This extends the previous work of the authors presented in References 18 and 31. The general methodology is applied to the re-formulation of some well known quadrilateral plate elements and some new triangular and quadrilateral plate elements which show promising features. Some examples of the good behaviour of these elements are given.     

A simple class of finite elements for plate and shell problems. I: Elements for beams and thin flat plates

This is the first paper of a pair which together discuss the development of a class of overlapping hinged bending finite elements which are suitable for the analysis of thin-shell, plate and beam structures. These elements rely on a simple physical analogy, involving overlapping hinged facets. They are based on quadratic overlapping assumed displacement functions. Only translational nodal degrees of freedom are necessary, which is a significant simplification over most other currently available beam, plate and shell finite elements which employ translational, rotational and higher-order nodal variables. In this paper the hinged bending element concept is introduced, and the hinged beam bending (HBB) and hinged plate bending (HPB) elements are formulated. In paper II these concepts are extended to develop a hinged shell bending (HSB) element. The HSB element can be readily combined with the constant strain triangular (CST) plane stress finite element for the modelling of thin-shell structures.     

A simple algorithm for the stiffness matrix of triangular plate bending elements

For a hierarchy of polynomials on the triangle there is derived an algorithm for computing the stiffness matrix of the plate bending element. The algorithm is easy to program and means a considerable saving of the computing time. The same approach can be used for any elliptic equation with constant coefficients.     

A simple triangular element for thick and thin plate and shell analysis

A new plate triangle based on Reissner–Mindlin plate theory is proposed. The element has a standard linear deflection field and an incompatible linear rotation field expressed in terms of the mid-side rotations. Locking is avoided by introducing an assumed linear shear strain field based on the tangential shear strains at the mid-sides. The element is free of spurious modes, satisfies the patch test and behaves correctly for thick and thin plate and shell situations. The element degenerates in an explicit manner to a simple discrete Kirchhoff form.     

Locking of thin plate/shell elements

Often, finite element solutions of thin plate/shell elements become very stiff and the displacement field solutions diverge from those predicted by Kirchhoff's theory. This phenomenon is known as the locking phenomenon. A theoretical fomulation demonstrating its existence is developed, and results of finite element analysis of a single element and mesh are discussed. This leads to a sufficient and necessary criterion which must be satisfied to avoid the locking phenomenon.     

Linked interpolation for Reissner-Mindlin plate elements: Part I—A simple quadrilateral

In most plate elements using the Reissner-Mindlin assumptions, the interpolations used for the lateral displacements (w) and the rotation (θ) involve the independent representation of each variable by its nodal values, usually with identical interpolations. To ensure a higher order of expansion for displacement w its representation is linked in the present paper with both sets of nodal variables. Conditions necessary for the use of such expansions are established here and the paper shows the development of a linear quadrilateral element (Q4BL) whose performance and robustness are good (although it possesses one singularity if only three degrees of freedom are prescribed). In Part II we apply the identical formulation to develop a triangular element (T3BL) which performs equally well and is fully robust.     

Linked interpolation for Reissner-Mindlin plate elements: Part II—A simple triangle

The formulation and shape functions given in Part I are extended to develop a simple plate bending triangle with good performance in both thin and thick situations. Indeed, its performance is better than that of other nine DOF elements and its computer implementation simpler. When used with selective reduced integration, the element produces identical results as that of Xu.^1,2 To save space, details given in Part I are not repeated and some results are also presented in the figures of Part I.     

A pure bending exact nodal-averaged shear strain method for finite element plate analysis

An averaged shear strain method, based on a nodal integration approach, is presented for the finite element analysis of Reissner–Mindlin plates. In this work, we combine the shear interpolation method from the MITC4 plate element with an area-weighted averaging technique for the nodal integration of shear energy to relieve shear locking in the thin plate analysis as well as to pass the pure bending patch test. In order to resolve the numerical instability caused by the direct nodal integration, the bending strain field is computed by a sub-domain nodal integration approach based on the Sub-domain Stabilized Conforming Integration and a modified curvature smoothing scheme. The resulting nodally integrated smoothed strain formulation is shown to contain only the primitive variables and thus can be easily implemented in the existing displacement-based finite element plate formulation. Several numerical examples are presented to demonstrate the accuracy of the present method.     

A simple chemical vapour deposition method for depositing thin TiO2 films

Thin films of TiO₂ were produced at 130–250°C by chemical vapour deposition (CVD) involving the hydrolysis of TiCl₄. An apparatus was developed which gives good control and reproducibility. The reaction takes place on a heated disc that rotates the silicon substrate. Premature reaction between the gases, TiCl₄ and water vapour is prevented by appropriate temperature control and careful design of the gas delivery system. With this apparatus the thickness of the TiO₂ films is controlled to within ±5% of the target value. Attention is also directed to reducing the pinhole density of the resulting films. The refractive index of the TiO₂ films was found to increase with increasing deposition temperature, from 2.1 at around 130°C to 2.4 at 250°C. From capacitance-voltage measurements the surface charge at the TiO₂-Si interface of films deposited at 200°C was found to be negative. Hence these TiO₂ films are good antireflection coatings for n-type metal/insulator/semiconductor inversionlayer solar cells.     

A simple chemical method for deposition of electrochromic Prussian blue thin films

This paper is about a recently developed new chemical method for deposition of Prussian blue thin films. The films are easily prepared by successive immersion of the substrates into an acidic aqueous solution of Fe₂(SO₄)₃ and K₄[Fe(CN)₆]. It is calculated of the results from AFM analysis that the growth in the film thickness by one immersion cycle corresponds to an average increase of 6 nm. The characterization of the films with X-ray diffraction, SEM-EDS analysis and FTIR spectroscopy shows that the deposited material is amorphous hydrated Fe₄[Fe(CN)₆]₃. The electrochromic properties are characterized by cyclic voltammetry and VIS spectrophotometry. The PB thin films exhibit stability and excellent reversibility, which make these films favorable for electrochromic devices.     

A simple class of finite elements for plate and shell problems. II: An element for thin shells,with only translational degrees of freedom

This paper is the second of a pair which discuss the development of a class of overlapping hinged bending finite elements, which are suitable for the analysis of thin-shell, plate and beam structures. These elements rely on a simple physically appealing analogy, in which overlapping hinged facets are used to represent bending effects. They are based on quadratic overlapping assumed displacement functions, which results in constant stress/strain representation. Only translational nodal degrees of freedom are necessary, which is a significant advantage over most other currently available beam, plate and shell finite elements which employ translational, rotational and higher-order nodal variables. In paper I the hinged bending element concept has been introduced, and the hinged beam bending (HBB) and hinged plate bending (HPB) elements formulated. In the present paper these concepts are extended to develop a hinged shell bending (HSB) element. The HSB element can be readily combined with the constant strain triangular (CST) plane stress finite element for the modelling of thin-shell structures; and the combined HSB-CST element is tested against a number of 'standard' thin-shell problems. The present paper, like paper I, is conducted entirely in the context of small-displacement elastic behaviour.     

Buckling of composite plates using simple shear flexible finite elements

An eight-noded, shear flexible quadratic rectangular element with five degrees of freedom per node is developed in this paper, to study the effects of transverse shear on the stability of layered composite plates, under uni-axial and bi-axial compression for various boundary conditions. Green's nonlinear strain tensor is used to formulate the initial stress matrix (K_σ). The validity of the element is demonstrated by comparing the results from the present formulation with those existing in the literature.     

Crushing of compact elements in impact interaction with a thin plate

On the basis of investigations it was established that the limit speeds of crushing are affected by the scale, the ductility and other physicomechanical properties of materials. Crushing is the result of one or several mutually interacting effects (intense plastic deformation, wave processes, and fields of residual stresses).Translated from Problemy Prochnosti, No. 4, pp. 51–57, April, 1994.     

A fast multipole boundary element method for solving the thin plate bending problem

A fast multipole boundary element method (BEM) for solving large-scale thin plate bending problems is presented in this paper. The method is based on the Kirchhoff thin plate bending theory and the biharmonic equation governing the deflection of the plate. First, the direct boundary integral equations and the conventional BEM for thin plate bending problems are reviewed. Second, the complex notation of the kernel functions, expansions and translations in the fast multipole BEM are presented. Finally, a few numerical examples are presented to show the accuracy and efficiency of the fast multipole BEM in solving thin plate bending problems. The bending rigidity of a perforated plate is evaluated using the developed code. It is shown that the fast multipole BEM can be applied to solve plate bending problems with good accuracy. Possible improvements in the efficiency of the method are discussed.     

A sector element for thin plate flexure

This paper presents a sector shape of an element ideally suited for the analysis of sectorial and annular plates. A conforming function with twenty degrees of freedom is developed in polar co-ordinates to represent the deformation of the element in bending. The finite element method is applied to some plate bending problems to illustrate the power and efficiency of sector elements.