Data processing: structural design – modeling – simulation – and em – Structural design
Reexamination Certificate
2000-10-16
2004-03-09
Paladini, Albert W. (Department: 2125)
Data processing: structural design, modeling, simulation, and em
Structural design
C703S007000, C700S098000
Reexamination Certificate
active
06704693
ABSTRACT:
TECHNICAL FIELD
The invention relates to a method and apparatus for the structural analysis of components, of particular but by no means exclusive application in determining the deformation and stress distribution within an object that is subject to loads, especially in the analysis of injection molded parts to determine their deformation and stress levels under external or internal loading.
This invention is of most particular application in the structural analysis of thin walled structures, the most important geometric feature of which is that one dimension, the thickness, is at least several times smaller than the other two dimensions. Examples of such structures are injection-molded parts of metal, ceramic or polymeric material, metal castings, and structures formed from sheet metal.
BACKGROUND
Manufacturers of components and parts, in particular by injection molding, prefer to move structural analysis of the parts upstream in the design process in order to reduce design costs and time-to-market. In order to satisfy the demands of design engineers, existing products integrate finite element analysis (FEA) and Computer Aided Drafting (CAD). Pro-Engineer (trade mark), CATIA (trade mark), I-DEAS (trade mark), Solid Works (trade mark) and Solid Edge (trade mark) brand solid modelling packages are commonly used in mechanical design and drafting. These packages may be used to generate three dimensional, photo-realistic descriptions (known as ‘solid models’) of the component geometry. At present, the structural analysis packages directly based on solid models use solid elements such as tetrahedra and hexahedra.
For structural analysis of solid models, the region defined by the solid model is divided into a plurality of small elements called solid elements. This process is called meshing and the resulting collection of solid elements is called a solid mesh. Solid elements are usually simple geometric solids such as tetrahedra or hexahedra. Generation of the solid mesh has been improved in recent years though for complex parts, it is rarely automatic. Frequently the user will need to remove features from the solid model to allow the mesh to be generated successfully. This can be very time consuming and in extreme cases may necessitate remodelling of the component or some region of the component.
The use of solid elements has no theoretical advantage over the use of shell elements for thin walled structures, at least in determining the structural response of the component under load. However, the majority of component modelling is done in solid modelling systems, so the use of solid elements is more natural and allows a better interface between the geometric solid model and the mesh used for analysis. A particular problem arises with components that are thin walled. In this case, to achieve accurate results, it has been necessary to ensure that there are several well-shaped solid elements in the thickness direction. This leads to a large number of elements in the model and hence long computing times and large memory requirements. While it may be possible to use a higher order element to reduce the number of elements through the thickness, the automatic generation of such a mesh is still difficult. To reduce the size of large solid element models, the user may increase the characteristic element dimension and remesh the geometry. The automatic mesh generator will then generate fewer elements but the resulting finite element mesh may not be able to model the real stress distribution, owing to too few elements. Moreover a solid element mesh with an insufficient number of elements through the thickness has other problems, such as ill-conditioned stiffness matrix, shear locking and poor simulation of pure-bending and bending-dominated structural response. These can seriously affect the reliability of finite element analysis.
Thin walled structures typically consist of plate and shell components. There exist several classical theories for plates and shells. Particularly well-known are the Kirchhoff theory and Mindlin-Reissner theory. In the Kirchhoff theory, it is assumed that normals to the mid-surface before deformation remain straight and normal to the mid-surface after deformation. The Mindlin-Reissner theory employs the hypothesis that normals to the mid-surfaces before deformation remain straight but not necessarily normal to the plate after deformation. The stress normal to the midsurface is disregarded in both theories. Many kinds of plate and shell elements have been established based on the different plate and shell theories over the past 35 years. These permit accurate finite element analysis of thin walled structures but require a model which must be derived from the solid geometry in the CAD system. A shell element model for analysis consists of a lattice of planar or curved shell elements. Generally the shape of the elements are of simple geometric shape such as triangles or quadrilaterals. The element thickness is not explicitly shown on the element, though it is a property of the element. A shell element model may be generated from a solid geometry by forming a mesh of shell elements on the imaginary surface lying between the outer walls of the solid model. This surface is frequently called the mid-plane surface of the solid model. It is not possible to define the mid-plane surface automatically in all cases, so the generation of a shell element model is frequently a laborious task involving the construction of a separate model for analysis.
Thus, the solid element approach to the structural analysis of a thin walled. component has the advantage of easy interfacing to the solid geometry, while the shell element approach has the advantages of good structural performance, low compute times, low memory requirements and ease of mesh generation. However, the solid element approach has the disadvantages of difficult mesh generation, high element number, long compute times, high memory requirements and poor results if insufficient elements through thickness for low order elements, while with the shell element approach it is difficult to derive a mid-plane for creating a shell mesh.
Existing boundary element methods permit structural analysis of components by using a mesh generated on the surface of the solid geometry, but traditional boundary element methods require that the material be isotropic and linear. Boundary element methods also lead to large unbanded systems of equations, the solution of which requires large amounts of memory.
As described above, the shell element is appropriate for the structural analysis of (generally thin walled) structures if the mid-plane model is available. Well-established plate-shell theories are used in the shell element so that the number of dimensions is reduced sensibly from three to two, i.e. from a solid to a surface. On the other hand, it is desirable to directly use the solid model from a CAD package for finite element analysis.
Such shell elements are generally triangular or quadrilateral in shape, and may be planar or curved. At each node there are 5 or 6 degrees of freedom (dof). The degrees of freedom, in the most general case, comprise three translations and three rotations.
FIG. 1
shows a triangular shell element which has a local coordinate system attached to it; the degrees of freedom are referenced to this coordinate system. Translational degrees of freedom for node n (n=1,2 or 3) in the local x, y and z directions are denoted by u
xn
, u
yn
and u
zn
respectively. Similarly rotations about the local x, y and z axes are denoted by &thgr;
xn
, &thgr;
yn
and &thgr;
zn
respectively. The surface through the element on which the nodes are located is called the reference surface. Usually a shell element is formulated with the midsurface as the reference surface. If the element reference surface is not on the midsurface, the element is said to be an eccentric shell element, with the distance by which the reference surface is displaced from the midsurface termed the eccentricity, &egr; (see FIG.
2
), in which is also indic
Fan Zhi Liang
Kennedy Peter Kenneth
Yu Hua Gang
Zheng Rong
Larson & Taylor PLC
Moldflow PTY LTD
Paladini Albert W.
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