A simple and efficient algorithm of automatic mesh generation for a general plate and frame structure with holes

The creation of the geometry for a general plate and frame structure with holes is discussed, and a simple and efficient algorithm of the mesh generation of the structure is presented for structural and thermal analysis. Mainly quadrilateral elements are generated and triangular elements are partially used in transient regions on the surface of the structure. For the frame parts of the structure, beam elements are generated for structural analysis and bar elements for conduction, convection and radiation for thermal analysis compatible with adjacent plate elements. A simple method to generate nodes at arbitrary point of the structure is also described.Numerical examples are given to demonstrate the effectiveness of the method on PC.     

Vibration of frames and other structures with banded stiffness matrix

A general digital computer method based on a Sturm sequence procedure is described for determining the natural frequencies and associated modes of undamped free vibration of frames and other structures whose stiffness and mass matrices are of band form. A program which uses the method for the analysis of plane multi-storey building frames is outlined, and numerical results are presented for a simple test case and for a 19-storey frame.     

方钢管混凝土框架-薄钢板剪力墙边框柱刚度研究

钢框架-薄钢板剪力墙竖向边缘构件刚度限值源于经典薄腹梁理论,其仅适用于钢框架,对于方钢管混凝土框架-薄钢板剪力墙,该刚度限值公式不再适用。该文基于薄腹梁理论,提出了方钢管混凝土竖向边缘构件的刚度限值计算公式。构建了不同宽高比和宽厚比分析模型,进行了非线性数值分析,研究了不同柱刚度对方钢管混凝土框架-薄钢板剪力墙力学性能、边框变形和破坏机制的影响。结果表明,按照该文公式设计的方钢管混凝土竖向边缘构件可充分发挥薄钢板剪力墙的结构性能,实现理想的破坏机制。     

Extended rotation‐free plate and beam elements with shear deformation effects

This paper describes a methodology for extending rotation‐free plate and beam elements to accounting for transverse shear deformation effects. The ingredients for the element formulation are a Hu–Washizu‐type mixed functional, a linear interpolation for the deflection and the shear angles over standard finite elements and a finite volume approach for computing the bending moments and the curvatures over a patch of elements. As a first application of the general procedure, we present an extension of the three‐noded rotation‐free basic plate triangle (BPT) originally developed for thin plate analysis to account for shear deformation effects of relevance for thick plates and composite‐laminated plates. The nodal deflection degrees of freedom (DOFs) of the original BPT element are enhanced with the two shear deformation angles. This allows to compute the bending and shear deformation energies leading to a simple triangular plate element with three DOFs per node (termed BPT+ element). For the thin plate case, the shear angles vanish and the element reproduces the good behaviour of the original thin BPT element. As a consequence the element is applicable to thick and thin plate situations without exhibiting shear locking effects. The numerical solution for the thick case can be found iteratively starting from the deflection values for the Kirchhoff theory using the original thin BPT element. A two‐noded rotation‐free beam element termed CCB+ applicable to slender and thick beams is derived as a particular case of the plate formulation. The examples presented show the robustness and accuracy of the BPT+ and the CCB+ elements for thick and thin plate and beam problems. Copyright © 2010 John Wiley & Sons, Ltd.     

Refined triangular discrete Mindlin flat shell elements

In this paper flat shell elements are formed by the assemblage of discrete Mindlin plate elements RDKTM and either the constant strain membrane element CST or the Allmans membrane element with drilling degrees of freedom LST. The element RDKTM is a robust Mindlin plate element, which can perform uniformly thick and thin plate bending analysis. It also passes the patch test for thin plate bending, and its convergence for very thin plates can be ensured theoretically. The singularity of the stiffness matrix and membrane locking are studied for the present elements. Numerical examples are presented to show that the present models indeed possess properties of simple formulations, high accuracy for thin and thick shells, and it is free from shear locking for thin plate/shell analysis.     

Analysis and design of the flexible composite membrane stretched on the spacecraft solar array frame

Nonlinear analysis of the deformation of a thin flexible composite membrane stretched on a rectangular cell of the spacecraft solar array frame is presented in the paper. The frame of the array and the thin flexible membrane stretched on this frame are designed to be capable of withstanding the transverse mechanical loadings exerted on the structure during the delivery to orbit and deployment. The governing nonlinear equations modelling the pre-stretched flexible orthotropic membrane are solved using Galerkin method. Results of calculations are compared with those based on finite-element modelling. The comparisons have demonstrated efficiency of the proposed approach to the analysis and design of composite solar arrays featuring orthotropic composite flexible membranes. The parametric analyses were performed for various combinations of the g-force, mass of the photovoltaic elements and dimensions of the solar array.     

Two simple and efficient displacement‐based quadrilateral elements for the analysis of composite laminated plates

Two simple 4‐node 20‐DOF and 4‐node 24‐DOF displacement‐based quadrilateral elements named RDKQ‐L20 and RDKQ‐L24 are developed in this paper based on the first‐order shear deformation theory (FSDT) for linear analysis of thin to moderately thick laminates. The deflection and rotation functions of the element sides are obtained from Timoshenko's laminated composite beam functions. Linear displacement interpolation functions of the standard 4‐node quadrilateral isoparametric plane element and displacement functions of a quadrilateral plane element with drilling degrees of freedom are taken as in‐plane displacements of the proposed elements RDKQ‐L20 and RDKQ‐L24, respectively. Due to the application of Timoshenko's laminated composite beam functions, convergence can be ensured theoretically for very thin laminates. The elements are simple in formulation, and shear‐locking free for extremely thin laminates even with full integration. A hybrid‐enhanced procedure is employed to improve the accuracy of stress analysis, especially for transverse shear stresses. Numerical tests show that the new elements are convergent, not sensitive to mesh distortion, accurate and efficient for analysis of thin to moderately thick laminates. Copyright © 2004 John Wiley & Sons, Ltd.     

A triangular finite element for thin plates and shells

A finite element modelling technique which utilizes a triangular element with 45 degrees-of-freedom and seven-point integration has been tested for analysis of thin plate and shell structures. The element is based on the degenerate solid shell concept and the mixed formulation with assumed independent inplane and transverse shear strains. Numerical result indicates effectiveness of the present modelling technique which features combined use of elements with kinematic modes and those without kinematic modes in an attempt to eliminate both locking and spurious kinematic modes at global structural level.     

Analysis of infilled frames using A coupled finite element and boundary element solution scheme

The behaviour of infilled frames subjected to horizontal loads is analysed by an iterative numerical procedure. The stiffness of the structural system is determined with variations in geometrical and mechanical characteristics. The analysis is carried out utilizing the boundary element method (BEM) for the infill and opportunely dividing the frame into finite elements, so as to transform the mutual interactions of the two subsystems into stresses distributed along the boundary for the infill and into nodal actions for the frame. This makes it possible to take into account the separation arising between the two substructures when mutual tensile stresses are involved. At first, infills without openings are considered, using BEM with constant elements for two-dimensional problems in elasticity. The results are compared with those obtained using the simplified equivalent pin-jointed strut model, which is very common in the literature. Subsequently, using an analogous procedure, panels with openings are considered. For these systems, for which no satisfactory simplified models exist, the loss of stiffness in relation to the size of the opening is evaluated.     

The identification and elimination of artificial stiffening errors in finite elements

The causes of shear locking and other discretization errors are analysed using a physically interpretable notation. This analysis provides insights that allow the errors due to shear locking to be removed either directly or indirectly. St. Venant's principle is incorporated into the stiffness matrix to directly eliminate shear locking from bending elements. Rules-of-thumb are suggested by the same analysis that will insure the absence of errors due to shear locking at the cost of additional degrees of freedom. It is also shown that aspect ratio stiffening in membrane elements is partially due to the same modelling error that produces shear locking. The source of parasitic shear is also identified and a direct procedure for eliminating it is given. A two node Timoshenko beam element and a four node membrane element are fully developed in symbolic form. The procedure is directly applicable to plate bending elements.     

防屈曲支撑加固钢筋混凝土框架的实用设计方法

防屈曲支撑可以显著减小地震作用下钢筋混凝土框架的层间变形需求,该文提出一种新的防屈曲支撑加固钢筋混凝土框架实用设计方法,以实现在增设防屈曲支撑的同时避免对构造措施不满足现行抗震设计规范要求的主体结构构件逐个进行局部加固这一抗震加固目标。首先提出层间承载力最薄弱柱和层间最弱塑性铰抗震思路来分别解决小震下结构构件承载力设计问题和大震下结构层间变形验算问题;然后给出了设计方法的具体设计流程;最后,将设计方法应用于一栋图书馆阅览楼抗震加固设计中,分析结果表明防屈曲支撑加固框架结构的承载力和层间变形均满足现行抗震规范要求,验证了提出的结构实用设计方法的有效性。研究成果可为防屈曲支撑加固钢筋混凝土结构的初步设计提供参考。     

Three-dimensional finite element for analysing thin plate/shell structures

A three-dimensional (3-D) hexahedron finite element is presented for the analysis of thin plate/shell structures. The element employs an explicit algebraic definition of six uniform (continuum) strains, six rigid body modes and classical Lagrange-Germain-Kirchhoff thin plate bending modes. Nine additional stiffness factors are used to control higher-order hourglass modes. The element may be used for plate/shell analyses where the flat plate assumptions are appropriate. Also it can easily be adapted to form transition elements to lower order 2-D elements, or to higher-order 3-D continuum elements. The stiffness matrix satisfies the geometric isotropy requirement, passes the patch test, and gives essentially identical response to either applied transverse corner forces or to twisting moments applied on the corner, a requirement of Kirchhoff's corner conditions for a classical thin plate. Several examples are presented to demonstrate the performance of this finite element.     

OPTIMUM DESIGN OF LATTICE PORTAL FRAMES

Lattice portal frame structures fabricated using hot rolled angle sections for corner leg members laced together are often very economical systems for industrial structures. There is considerable flexibility in the design of such structures in terms of the spacings between and the unsupported lengths of corner leg members, besides the areas of the different elements of the frame. The minimum weight design of these frames is a nonlinear optimization problem which has been solved by using Rosen's gradient projection method. A computer program OPTFRAM, developed for the minimum weight design of lattice portal frames used in industrial structures, is described. This paper also presents the results of a parametric study carried out using the (OPTFRAM) computer program. Regression equations obtained from this study arc presented for use in day to day design.     

Structural behaviour of sandwich panel shear walls: An experimental analysis

Within a comprehensive research project devoted to analyse the contributing effect of cladding panels on the structural behaviour of steel frames under horizontal loads, a suitable experimental procedure has been set up in order to characterise the main behavioural parameters of specific shear walls. In particular, with regard to light-weight sandwich panels, which are currently used in building as enclosure elements, monotonic and cyclic full-scale shear tests have been performed on both single connection specimens and pin-jointed steel frames branced by infill panels. Such an activity, whose main results are summarised in this paper, firstly provides the experimental evidence as basis for setting up numerical and analytical intepretative models. Besides, it supplies useful information on the possibility to use this panel typology as shear wall components. Finally, it points out how their shear performance can be improved through simple modifications of standard prototypes.     

内填钢板墙双肢冷轧C型钢框架抗震性能

内填钢板墙的双肢C型钢框架是一种新型的框架结构体系,建立三层该类框架进行低周往复加载试验,分析其破坏形态、模式及抗震性能,试验结果表明:钢板墙的屈曲起到了良好的耗能作用,内填钢板墙可以提高双肢C型钢框架的承载力和刚度,层间位移角满足抗震设计要求。在试验的基础上,考虑钢板墙的高厚比、钢板墙高宽比、框架柱刚度系数等参数,采用验证后的有限元模型,分析各个参数下内填钢板墙框架的抗震性能,得到了一定的参数设计建议。     

Consistent multiscale analysis of heterogeneous thin plates with smoothed quadratic Hermite triangular elements

A consistent multiscale formulation is presented for the bending analysis of heterogeneous thin plate structures containing three dimensional reinforcements with in-plane periodicity. A multiscale asymptotic expansion of the displacement field is proposed to represent the in-plane periodicity, in which the microscopic and macroscopic thickness coordinates are set to be identical. This multiscale displacement expansion yields a local three dimensional unit cell problem and a global homogenized thin plate problem. The local unit cell problem is discretized with the tri-linear hexahedral elements to extract the homogenized material properties. The characteristic macroscopic deformation modes corresponding to the in-plane membrane deformations and out of plane bending deformations are discussed in detail. Thereafter the homogenized material properties are employed for the analysis of global homogenized thin plate with a smoothed quadratic Hermite triangular element formulation. The quadratic Hermite triangular element provides a complete C¹ approximation that is very desirable for thin plate modeling. Meanwhile, it corresponds to the constant strain triangle element and is able to reproduce a simple piecewise constant curvature field. Thus a unified numerical implementation for thin plate analysis can be conveniently realized using the triangular elements with discretization flexibility. The curvature smoothing operation is further introduced to improve the accuracy of the quadratic Hermite triangular element. The effectiveness of the proposed methodology is demonstrated through numerical examples.     

A family of simple and robust finite elements for linear and geometrically nonlinear analysis of laminated composite plates

A family of simple, displacement-based and shear-flexible triangular and quadrilateral flat plate/shell elements for linear and geometrically nonlinear analysis of thin to moderately thick laminate composite plates are introduced and summarized in this paper.

The developed elements are based on the first-order shear deformation theory (FSDT) and von-Karman’s large deflection theory, and total Lagrangian approach is employed to formulate the element for geometrically nonlinear analysis. The deflection and rotation functions of the element boundary are obtained from Timoshenko’s laminated composite beam functions, thus convergence can be ensured theoretically for very thin laminates and shear-locking problem is avoided naturally.

The flat triangular plate/shell element is of 3-node, 18-degree-of-freedom, and the plane displacement interpolation functions of the Allman’s triangular membrane element with drilling degrees of freedom are taken as the in-plane displacements of the element. The flat quadrilateral plate/shell element is of 4-node, 24-degree-of-freedom, and the linear displacement interpolation functions of a quadrilateral plane element with drilling degrees of freedom are taken as the in-plane displacements.

The developed elements are simple in formulation, free from shear-locking, and include conventional engineering degrees of freedom. Numerical examples demonstrate that the elements are convergent, not sensitive to mesh distortion, accurate and efficient for linear and geometric nonlinear analysis of thin to moderately thick laminates.     

Parametric representation of weld fillets using shell finite elements—a proposal based on minimum stiffness and inertia errors

The objective of the present work is to introduce a methodology capable of modelling welded components for structural stress analysis. The modelling technique was based on the recommendations of the International Institute of Welding; however, some geometrical features of the weld fillet were used as design parameters in an optimization problem. Namely, the weld leg length and thickness of the shell elements representing the weld fillet were optimized in such a way that the first natural frequencies were not changed significantly when compared to a reference result. Sequential linear programming was performed for T-joint structures corresponding to two different structural details: with and without full penetration weld fillets. Both structural details were tested in scenarios of various plate thicknesses and depths. Once the optimal parameters were found, a modelling procedure was proposed for T-shaped components. Furthermore, the proposed modelling technique was extended for overlapped welded joints. The results obtained were compared to well-established methodologies presented in standards and in the literature. The comparisons included results for natural frequencies, total mass and structural stress. By these comparisons, it was observed that some established practices produce significant errors in the overall stiffness and inertia. The methodology proposed herein does not share this issue and can be easily extended to other types of structure.     

Refined 9‐Dof triangular Mindlin plate elements

Based on the Mindlin/Reissner plate theory, two refined triangular thin/thick plate elements, the conforming displacement element DKTM with one point quadrature for the part of shear strain and the element RDKTM with the re‐constitution of the shear strain, are proposed. In the formulations the exact displacement function of the Timoshenko's beam is used to derive the element displacements of the refined elements. Numerical examples are presented to show that the present models indeed possess properties of high accuracy for thin and thick plates, is capable of passing the patch test required for Kirchhoff thin plate elements, and does not exhibits extra zero energy modes. The element RDKTM is free of locking for very thin plate analysis and its convergence can be ensured theoretically. However, the element DKTM is not free of shear locking when the thickness/span ratios less than 10^?2. Copyright © 2001 John Wiley & Sons, Ltd.