Optimal blank design based on finite element method for blades of large Francis turbines

Metal pressing process that is widely used in industries has advantages over casting process for producing large Francis turbine blades from thick plates. Prior to the pressing process, blank design is firstly performed to determine flat blanks. The traditional trial and error approach is not applicable to blade design for Francis turbines that are not standard due to hydraulic characteristics of power plant sites. The rapid development of computing technology makes it possible to obtain optimal flat blanks by numerical modelling and simulation. In this paper, inverse finite element approach is investigated for blank design and an elasto-plastic model has been built using the well-known commercial software ANSYS. Numerical simulations for blade unfolding models with thick shell elements, solid elements and shell elements have given results with negligible differences. Unfolding tests with simple geometries have been carried out and the numerical results agree well with the analytical solutions. A large and thick shape of a Francis turbine blade for a hydropower plant has been successfully unfolded by inverse FE model. Sensibility analysis shows that the middle surface of the flat blank is independent of blade thickness. For ensuring the machining of the blade after the pressing process, a new contour is obtained by extending the boundary of the flat blank provided by the numerical model. This research may provide a useful tool for optimal blank design of Francis turbine blades.     

叉车三维实体造型及CAD

在实体造型系统上建立了叉车的三维实体模型,并对部分零 部件进行了运动学、动力学仿真及有限元分析计算,得到叉车综合效能方面的有关评价资料 ,可作为对已有设计的检验,且为改进设计提供依据。     

夹层板系统碰撞性能数值仿真分析技术

为促进夹层板系统（Sandwich Plate System,SPS）在船舶耐撞结构设计中的应用,用Abaqus分析SPS在碰撞载荷下的数值模型化技术,包括夹芯层和面板的建模方式、连接形式和网格尺寸．根据该技术研究SPS在碰撞冲击载荷作用下的力学性能,如结构损伤变形、碰撞力和结构吸能等．结果表明,SPS建模采用壳一体混合模型（即上、下面板采用壳单元,夹芯层采用体单元）较合理;夹芯层与面板之间采用绑定连接较合理;SPS具有良好的耐撞性能．     

New quadratic solid–shell elements and their evaluation on linear benchmark problems

This paper is concerned with the development of a new family of solid–shell finite elements. This concept of solid–shell elements is shown to have a number of attractive computational properties as compared to conventional three-dimensional elements. More specifically, two new solid–shell elements are formulated in this work (a fifteen-node and a twenty-node element) on the basis of a purely three-dimensional approach. The performance of these elements is shown through the analysis of various structural problems. Note that one of their main advantages is to allow complex structural shapes to be simulated without classical problems of connecting zones meshed with different element types. These solid–shell elements have a special direction denoted as the “thickness”, along which a set of integration points are located. Reduced integration is also used to prevent some locking phenomena and to increase computational efficiency. Focus will be placed here on linear benchmark problems, where it is shown that these solid–shell elements perform much better than their counterparts, conventional solid elements.     

An open platform of shape design optimization for shell structure

A general platform built on a computer-aided design (CAD) system is developed for parameterized shape design optimization of shell structure. Within the platform, parameterized surface modeling and computer-aided engineering (CAE) applications are embedded and seamlessly integrated with the CAD system through its application programming interface (API). Firstly, instead of the CAD system inherent surface modeling, a parameterized surface modeling for shell structure is fulfilled through integrating with parametric solid modeling of the CAD system. Thus, any dimensions for parametric solid modeling can be used to control shape modification of shell structure and serve as design variables for shape design optimization. Secondly, seamless integration of geometry modeling and finite-element modeling for shell structure is implemented. Finally, with integrated procedures of finite-element analysis and optimization algorithms, a general platform for parameterized shape optimization of shell structure is realized. Numerical examples are presented, and the results validate the effectiveness and efficiency of the platform. A shorten version of this paper was presented to the 7th World Congress of Computation Mechanics (WCCM 2006), July 16–22, 2006, Los Angeles, CA, USA.     

The usefulness of static condensation in the finite element analysis of stiffened submersible cylindrical hulls

The usefulness of the static condensation technique in the finite element analysis of stiffened submersible. cylindrical hulls is examined in this paper. The finite element formulation used herein is essentially the same as outlined by the authors in an earlier paper wherein the stiffener is modeled rigorously using axisymmetric thin annular plate elements for the web and axisymmetric thin shell elements for the flange. The static condensation technique has been applied in this paper to reduce these stiffener finite elements so that their effect can be transferred to the shell node at the point of attachment of the stiffener with the shell. The advantage of such condensation of the stiffener elements is the smaller number of equations to be solved without the rigor of the stiffener modeling being lost in any way. The manner of incorporating the condensation in the computer program has been described. Examples of several stiffened submersible cylindrical hulls have been considered as an illustration of the use of the program.     

A general isoparametric finite element program SDRC SUPERB

SDRC SUPERB is a general purpose finite element program that performs linear static, dynamic and steady state heat conduction analyses of structures made of isotropic and/or orthotropic elastic materials having temperature dependent properties. The finite element library of SUPERB contains isoparametric plane stress, plane strain, flat plate, curved shell, solid type curved shell and solid elements in addition to conventional beam and spring elements. Linear, quadratic and cubic interpolation functions are available for all isoparametric elements. Independent parameters such as displacements and temperatures are obtained from SUPERB using the stiffness method of analysis. The remaining dependent parameters, such as stresses and strains, are evaluated at element gauss points and extrapolated to nodal locations. Averaged values are given as final output. The graphic capabilities of SUPERB consists of geometry and distorted geometry plotting, and stress, strain and temperature contouring. Contours are plotted at user defined cutting planes for solids and at top, middle or bottom surfaces for plate and shell types of structures.In the first part of this paper, the program capabilities of SUPERB are summarized. Extrapolation techniques used for determining dependent nodal parameters and for contour plotting are explained in the second part of the paper. Behavior of standard, wedge and transition type isoparametric elements and the effect of interpolation function orders on accuracy are discussed in the third part. The results of several illustrative problems are included.     

Geometrically non-linear formulation for the three dimensional solid-shell transition finite elements

This paper presents a geometrically non-linear formulation using total lagrangian approach for the solid-shell transition finite elements. Such transition finite elements are necessary in geometrically non-linear analysis of structures modelled with three dimensional solid elements and the curved shell elements. These elements are an essential connecting link between the solid elements and the shell elements. The element formulation presented here is derived using the properties of the three dimensional solid elements and the curved shell elements. No restrictions are imposed on the magnitude of the nodal rotations. Thus the element formulation is capable of handling large rotations between two successive load increments. The element properties are derived and presented in detail. Numerical examples are also presented to demonstrate their behavior, accuracy and applications in three dimensional stress analysis.

It is shown that the selection of different stress and strain components at the integration points do not effect the overall linear response of the element. However, in geometrically non-linear applications it may be necessary to select appropriate stress and the strain components at the integration points for stable and converging element behavior. Numerical examples illustrate various characteristics of the element.     

Reinforced steel I-beams: A comparison between 2D and 3D simulation

This study reports the accuracies of Finite Element (FE) simulations, based on two and three dimensional (2D and 3D) modelling of strengthened steel I-beams in static linear and non-linear analyses. To investigate the effects of simulation modelling methods on the accuracy of the results, 28 computer and laboratory specimens were used. To strengthen the beams, Carbon Fibre Reinforced Polymer (CFRP) and steel plates were applied, and to simulate the specimens, ANSYS software was utilized. All specimens were modelled by using shell elements or solid elements in the 2D and 3D modelling cases, respectively. The results show that non-linear and 3D simulation methods predicted the experimental results appropriately.     

有限元法在板料二次成形中的应用

本文建立了板料成形动力显式有限元模拟，采用四节点退化壳单元对板料进行离散化，利用中心差分法离散时间域，建立显式计算格式，采用罚函数法和修正库仑定理计算接触力和摩擦力。对二次成形过程，建立了有限元分析计算模型。通过Dynaform对板料成形进行仿真得出最后结论。     

Transition finite elements with temperature and temperature gradients as primary variables for axisymmetric heat conduction

This paper presents finite element formulation for a special class of elements referred to as “transition finite elements” for axisymmetric heat conduction. The transition elements are necessary in applications requiring the use of both axisymmetric solid elements and axisymmetric shell elements. The elements permit transition from the solid portion of the structure to the shell portion of the structure. A novel feature of the formulation presented here is that nodal temperatures as well as nodal temperature gradients are retained as primary variables. The weak formulation of the Fourier heat conduction equation is constructed in the cylindrical co-ordinate system (r, z). The element geometry is defined in terms of the co-ordinates of the nodes as well as the nodal point normals for the nodes lying on the middle surface of the element. The element temperature field is approximated in terms of element approximation functions, nodal temperatures and the nodal temperature gradients. The properties of the transition elements are then derived using the weak formulation and the element temperature approximation. The formulation presented here permits linear temperature distribution through the element thickness. Convective boundaries as well as distributed heat flux is permitted on all four faces of the element. Furthermore, the element formulation also permits distributed heat flux and orthotropic material behaviour. Numerical examples are presented, first to illustrate the accuracy of the formulation and second to demonstrate its usefulness in practical applications. Numerical results are also compared with the theoretical solutions.     

Coupling geological and numerical models to simulate groundwater flow and contaminant transport in fractured media

A new modeling approach is presented to improve numerical simulations of groundwater flow and contaminant transport in fractured geological media. The approach couples geological and numerical models through an intermediate mesh generation phase. As a first step, a platform for 3D geological modeling is used to represent fractures as 2D surfaces with arbitrary shape and orientation in 3D space. The advantage of the geological modeling platform is that 2D triangulated fracture surfaces are modeled and visualized before building a 3D mesh. The triangulated fractures are then transferred to the mesh generation software that discretizes the 3D simulation domain with tetrahedral elements. The 2D triangular fracture elements do not cut through the 3D tetrahedral elements, but they rather form interfaces with them. The tetrahedral mesh is then used for 3D groundwater flow and contaminant transport simulations in discretely fractured porous media. The resulting mesh for the 2D fractures and 3D rock matrix is checked to ensure that there are no negative transmissibilities in the discretized flow and transport equation, to avoid unrealistic results. To test the validity of the approach, flow and transport simulations for a tetrahedral mesh are compared to simulations using a block-based mesh and with results of an analytical solution. The fluid conductance matrix for the tetrahedral mesh is also analyzed and compared with known matrix values.     

Computer modeling for the coupled stress-wave and structural response

The mesh density and the time-step size requirements of a Finite Element Model used to predict the coupled stress-wave and the structural response to dynamic loading are discussed. The problem chosen for this study is a long cylindrical shell containing a bonded annular solid core subjected to external uniform radial impulse. This shell-core system represents the case and solid propellant of a solid rocket motor. Depending on the geometry and the mechanical properties of the shell-core system, the coupling between the radial stress-waves in the core and the gross structural breathing mode of the shell-core system could be either strong or weak.

When the time required for a through the thickness round trip of radial stress waves in the core is of the same order of magnitude as the gross structural breathing mode period of the whole system, the coupling between the stress-wave propagation and the structural response is strong. A finer mesh of solid elements (NASTRAN HEXA elements) for modeling the solid core is required to predict correctly the peak hoop strains and stresses in the shell. A coarser mesh gives erroneous results.

On the other hand, when the time required for a through the thickness round trip of radial waves is small compared to the structural breathing mode period of the system, the coupling between the wave propagation and the structural response is weak and the two are decoupled. In this case, a coarser mesh of solid elements gives a good estimate of the peak hoop stresses in the shell. These values are not significantly changed if the mesh is made finer.     

Three dimensional solid-shell transition finite elements for heat conduction

This paper presents a finite element formulation for a special class of finite elements referred to as ‘Solid-Shell Transition Finite Elements’ for three dimensional heat conduction. The solid-shell transition elements are necessary in applications requiring the use of both three dimensional solid elements and the curved shell elements. These elements permit transition from the solid portion of the structure to the shell portion of the structure. A novel feature of the formulation presented here is that nodel temperatures as well as nodal temperature gradients are retained as primary variables. The element geometry is defined in terms of coordinates of the nodes as well as the nodal point normals for the nodes lying on the middle surface of the element. The temperature field with the element is approximated in terms of element approximation functions, nodal temperatures and nodal temperature gradients. The properties of the transition element are then derived using the weak formulation (or the quadratic functional) of the Fourier heat conduction equation in the Cartesian coordinate system and the element temperature approximation. The formulation presented here permits linear temperature distribution in the element thickness direction.

Convective boundaries as well as distributed heat flux is permitted on all six faces of the elements. Furthermore, the element formulation also permits internal heat generation and orthotropic material behavior. Numerical examples are presented firstly to illustrate the accuracy of the formulation and secondly to demonstrate its usefulness in practical application. Numerical results are also compared with the theoretical solutions.     

Multi-layer multi-director concepts for D-adaptivity in shell theory

Solid mechanics problems use to be formulated in tensor notation in three-dimensional (3D) Euclidean space. But engineering practice favors reduced dimensional models, in order to describe deformation processes in its most natural way by surface- and line-like geometries, mainly for ease of error controling.Modern surface-like structures, e.g. shells, often show a layered structure or are computed––in case of inelastic materials––by use of virtual layers. The present paper thus is devoted to shells in layered representation. After demonstrating the equivalence of six-parameter, 4-noded shell elements with 3D hexahedron elements as fundamental model constituents, the treatment introduces two different layer-wise refinement concepts, one for modeling of complicated stress profiles, the other one for improvement of model deformability. Such concepts admit the simulation of rather arbitrary shell responses including all kinds of perturbations, like thickness jumps, points of single loads or loci of material damage. In order to validate this model, the paper will systematically transform all sets of basic mechanical conditions of a 3D solid of arbitrary material into corresponding two-dimensional sets of a multi-director shell theory. Aim is the evaluation of bounds for the convergence error.     

形状特征局部操作在实体造型中的实现

文章介绍了实体造型中形状特征的局部操作,研究了包含形状特征描述的数据结构,分析了形状特征的分类、框架、特征间的联系及有关操作,分析了欧拉运算及实现思路,在此基础上对实体造型进行局部操作,提高了造型中的运算效率,也对特征造型作了相应的探讨。     

Analysis and optimal design of plates and shells under dynamic loads – I: finite element and sensitivity analysis

In this paper we consider the development, integration, and application of reliable and efficient computational tools for the geometry modeling, mesh generation, structural analysis, and sensitivity analysis of variable-thickness plates and free-form shells under dynamic loads. A flexible shape-definition tool for surface modeling using Coons patches is considered to represent the shape and the thickness distribution of the structure, followed by an automatic mesh generator for structured meshes on the shell surface. Nine-node quadrilateral Mindlin–Reissner shell elements degenerated from 3D elements and with an assumed strain field, the so-called Huang–Hinton elements, are used for the FE discretization of the structure. The Newmark direct integration algorithm is used for the time discretization of the dynamic equilibrium equations for both the structural analysis and the semi-analytical (SA) sensitivity analysis. Alternatively, the sensitivities are computed by using the global finite difference (FD) method. Several examples are considered. In a companion paper, the tools presented here are combined with mathematical programming algorithms to form a robust and reliable structural optimization process to achieve better dynamic performance on the shell designs.     

Shape optimization of three-dimensional shell structures with the shape parametrization of a CAD system

This paper presents a method for shape optimization of flat or curved 3D shell structures, that takes advantage of the geometric modelling and automatic meshing capabilities of an existing parametric/associative CAD system. It is an extension of a method previously proposed by the authors for shape optimization of 2D and 3D solid structures. The implementation of the shell elements used is outlined, as well as the calculation of analytical sensitivities with the discrete method. The validity of the method is demonstrated with the optimization of two complex 3D shell structures.     

用三维实体单元分析薄壁箱型结构应注意的问题

从四边固定正方形板受均布载荷的经典问题入手,结合不同类型单元的特点,探讨应用三维实体单元分析薄壁箱型结构时应注意的几个问题,纠正三维实体单元分析和应用的误区,为提高结构分析计算结果精度提供参考.