Tetrahedron Elements with Linearly Varying Strain for the Matrix Displacement Method

1965 ◽  
Vol 69 (660) ◽  
pp. 877-880 ◽  
Author(s):  
J. H. Arcyris,

The author mentioned in his Main Lecture(1) the success achieved in the analysis of three-dimensional media, for small and large displacements, as well as anisotropic and non-elastic behaviour, by the introduction of tetrahedron elements of constant strain and stress(2), see also technical note 1 of this series(3). A cardinal point of the theory is the specification of natural strains, stresses and stiffness. At the same time attention was drawn to certain difficulties arising in the interpretation of the stresses at the nodal or other points, which are more severe than for constant strain triangles, the corresponding elements in the two-dimensional case. It was suggested in the lecture that a considerable improvement might be achieved by the specification of a linearly varying strain or stress state within the tetrahedron. The solution of this problem, limited to small displacements, is summarised in this fifth technical note and its application is to be demonstrated on an example in the printed lecture.

1969 ◽  
Vol 73 (697) ◽  
pp. 55-65 ◽  
Author(s):  
J. H. Argyris ◽  
D. W. Scharpf

It is by now well established that the computational analysis of significant problems in structural and continuum mechanics by the matrix displacement method often requires elements of higher sophistication than used in the past. This refers, in particular, to regions of steep stress gradients, which are frequently associated with marked changes in geometry, involving rapid variations of the radius of curvature. The philosophy underlying the idealisation of such configurations into finite elements was discussed in broad terms in ref. 1. It was emphasised that the so successful, constant strain, two-dimensional TRIM 3 and three-dimensional TET 4 elements do not, in general, prove the best choice. For this reason elements with a linear variation of strain like TRIM 6 and TET 10 were originally evolved and followed up with the quadratic strain elements TRIM 15, TRIA 4 (two-dimensional) and TET 20, TEA 8 (three-dimensional) of ref. 2. However, all these elements are characterised by straight edges and necessitate a polygonisation or polyhedrisation in the idealisation process. This may not be critical in many problems, but is sometimes of doubtful validity in the immediate neighbourhood of a curved boundary, where stress concentrations are most pronounced. To overcome this difficulty with a significant (local) increase of elements does not always yield the most economical and technically satisfactory solution. Moreover, there arises another inevitable shortcoming when dealing with TRIM and TET elements with a linear or quadratic variation of strain. Indeed, while TRIM 3 and TET 4 elements permit a very elegant extension into the realm of large displacements, this is not possible for the higher order TRIM and TET elements. This is simply due to the fact that TRIM 3 and TET 4 elements, by virtue of their specification, always remain straight under any magnitude of strain, but this is not so for the triangular and tetrahedron elements of higher sophistication.


1965 ◽  
Vol 69 (657) ◽  
pp. 633-636 ◽  
Author(s):  
J . H. Argyris

The author presented in his recent main lecture to the Society, “The Computer Shapes the Theory”, a number of novel developments in the matrix displacement method. Since the publication of the lecture and discussion will inevitably be delayed and cannot but illustrate the application of the new ideas on a series of examples, he has been repeatedly urged to summarise some of the more important theoretical contributions in the form of Technical Notes. The first deals with the elasto-plastic analysis, in the presence of strain hardening, of arbitrary three-dimensional configurations. The reader is assumed to be familiar with the corresponding elastic analysis given in refs. 2 and 3, where the medium is represented by a suitable assembly of tetrahedra under constant stress and strain. The corresponding two-dimensional case is investigated on the basis of triangles. Arbitrary anisotropic behaviour and large displacements were also included in refs. 2 and 3.


1982 ◽  
Vol 92 (3) ◽  
pp. 747-752 ◽  
Author(s):  
WS Haston ◽  
JM Shields ◽  
PC Wilkinson

The adhesion and locomotion of mouse peripheral lymph node lymphocytes on 2-D protein- coated substrata and in 3-D matrices were compared. Lymphocytes did not adhere to, or migrate on, 2-D substrata suck as serum- or fibronectin-coated glass. They did attach to and migrate in hydrated 3-D collagen lattices. When the collagen was dehydrated to form a 2-D surface, lymphocyte attachment to it was reduced. We propose that lymphocytes, which are poorly adhesive, are able to attach to and migrate in 3-D matrices by a nonadhesive mechanism such as the extension and expansion of pseudopodia through gaps in the matrix, which could provide purchase for movement in the absence of discrete intermolecular adhesions. This was supported by studies using serum-coated micropore filters, since lymphocytes attached to and migrated into filters with pore sizes large enough (3 or 8 mum) to allow pseudopod penetration but did not attach to filters made of an identical material (cellulose esters) but of narrow pore size (0.22 or 0.45 mum). Cinematographic studies of lymphocyte locomotion in collagen gels were also consistent with the above hypothesis, since lymphocytes showed a more variable morphology than is typically seen on plane surfaces, with formation of many small pseudopodia expanded to give a marked constriction between the cell and the pseudopod. These extensions often remained fixed with respect to the environment as the lymphocyte moved away from or past them. This suggests that the pseudopodia were inserted into gaps in the gel matrix and acted as anchorage points for locomotion.


2018 ◽  
Vol 25 (9) ◽  
pp. 3386-3405 ◽  
Author(s):  
Maryam Hassani ◽  
Arash Shahin ◽  
Manouchehr Kheradmandnia

Purpose The purpose of this paper is to examine the application of C-shaped QFD 3D Matrix in comparing process characteristics (PC), performance aspects (PA) and customer requirements, simultaneously and to prioritize the first two sets, respectively. Design/methodology/approach A three dimensional matrix has been developed with three sets of PC, PA and customers’ requirements and C-shaped matrix has been applied for simultaneous comparison of the dimensions and prioritization of the subsets of PC and PA. The proposed approach has been examined in a post bank. Findings Findings confirm the possibility of simultaneous comparison and prioritization of the three sets of dimensions of this study in post bank services. In addition, “growth and learning” and “bilateral relationship with suppliers” had the first priorities among PA and PC, respectively. Research limitations/implications While the proposed approach has many advantages, filling the matrixes is time-consuming. Since illustrating the 3D matrix was not possible, the matrix was separated into five two-dimensional matrixes. Originality/value Compared to the studied literature, the proposed approach is practically new in the post bank services.


F1000Research ◽  
2016 ◽  
Vol 5 ◽  
pp. 1819 ◽  
Author(s):  
Francois Bordeleau ◽  
Cynthia A. Reinhart-King

There has been immense progress in our understanding of the factors driving cell migration in both two-dimensional and three-dimensional microenvironments over the years. However, it is becoming increasingly evident that even though most cells share many of the same signaling molecules, they rarely respond in the same way to migration cues. To add to the complexity, cells are generally exposed to multiple cues simultaneously, in the form of growth factors and/or physical cues from the matrix. Understanding the mechanisms that modulate the intracellular signals triggered by multiple cues remains a challenge. Here, we will focus on the molecular mechanism involved in modulating cell migration, with a specific focus on how cell contractility can mediate the crosstalk between signaling initiated at cell-matrix adhesions and growth factor receptors.


2007 ◽  
Vol 17 (04) ◽  
pp. 593-615 ◽  
Author(s):  
J. ELSCHNER ◽  
H.-C. KAISER ◽  
J. REHBERG ◽  
G. SCHMIDT

Let ϒ be a three-dimensional Lipschitz polyhedron, and assume that the matrix function μ is piecewise constant on a polyhedral partition of ϒ. Based on regularity results for solutions to two-dimensional anisotropic transmission problems near corner points we obtain conditions on μ and the intersection angles between interfaces and ∂ϒ ensuring that the operator -∇ · μ∇ maps the Sobolev space [Formula: see text] isomorphically onto W-1,q(ϒ) for some q > 3.


1968 ◽  
Vol 72 (691) ◽  
pp. 613-617 ◽  
Author(s):  
J. H. Argyris ◽  
I. Fried ◽  
D. W. Scharpf

The description of the LUMINA element in T.N. 11 is followed by another three-dimensional interpolation element, called HERMES 8, available in the ASKA language and briefly mentioned in ref. 1. Just as the LUMINA set, the HERMES element represents a general hexahedronal element with curved faces and has proved a most useful component block for three-dimensional analysis of complex bodies. The cardinal idea underlying the HERMES development aims at combining the advantages of the Lagrangian and Hermitian interpolation techniques.


1977 ◽  
Vol 99 (4) ◽  
pp. 828-834 ◽  
Author(s):  
J. A. Kirk ◽  
D. K. Anand ◽  
C. McKindra

Matrix geometry techniques are applied to predicting three-dimensional cutting forces. In the present model a specific cutting plane is located and two-dimensional metal cutting theory is applied. Force predictions in this plane are then matrix transformed to three orthogonal forces acting on the cutting tool. Experimental results show the matrix model accurately predicts three-dimensional cutting forces in turning of long slender workpieces. Experimental results are also compared to other analytical models described in the literature.


2009 ◽  
Vol 65 (3) ◽  
pp. 300-307 ◽  
Author(s):  
G. D. Ilyushin ◽  
V. A. Blatov

A combinatorial topological analysis is carried out by means of the program package TOPOS4.0 [Blatov (2006), IUCr Comput. Commun. Newsl. 7, 4–38] and the matrix self-assembly is modeled for crystal structures of the ZrZn22 family (space group Fd\bar 3m, Pearson code cF184), including the compounds with superstructural ordering. A number of strict rules are proposed to model the crystal structures of intermetallics as a network of cluster precursors. According to these rules the self-assembly of the ZrZn22-like structures was considered within the hierarchical scheme: primary polyhedral cluster → zero-dimensional nanocluster precursor → one-dimensional primary chain → two-dimensional microlayer → three-dimensional microframework (three-dimensional supraprecursor). The suprapolyhedral cluster precursor AB 2 X 37 of diameter ∼ 12 Å and volume ∼ 350 Å3 consists of three polyhedra (one AX 16 of the \bar 43m point symmetry and two regular icosahedra BX 12 of the \bar 3m point symmetry); the packing of the clusters determines the translations in the resulting crystal structure. A novel topological type of the two-dimensional crystal-forming 4,4-coordinated binodal net AB 2, with the Schläfli symbols 3636 and 3366 for nodes A and B, is discovered. It is shown that the ZrZn22 superstructures are formed by substituting some atoms in the cluster precursors. Computer analysis of the CRYSTMET and ICSD databases shows that the cluster AB 2 X 37 occurs in 111 intermetallics belonging to 28 structure types.


2021 ◽  
Author(s):  
Ray Chapman ◽  
Phu Luong ◽  
Sung-Chan Kim ◽  
Earl Hayter

The Environmental Laboratory (EL) and the Coastal and Hydraulics Laboratory (CHL) have jointly completed a number of large-scale hydrodynamic, sediment and water quality transport studies. EL and CHL have successfully executed these studies utilizing the Geophysical Scale Transport Modeling System (GSMB). The model framework of GSMB is composed of multiple process models as shown in Figure 1. Figure 1 shows that the United States Army Corps of Engineers (USACE) accepted wave, hydrodynamic, sediment and water quality transport models are directly and indirectly linked within the GSMB framework. The components of GSMB are the two-dimensional (2D) deep-water wave action model (WAM) (Komen et al. 1994, Jensen et al. 2012), data from meteorological model (MET) (e.g., Saha et al. 2010 - http://journals.ametsoc.org/doi/pdf/10.1175/2010BAMS3001.1), shallow water wave models (STWAVE) (Smith et al. 1999), Coastal Modeling System wave (CMS-WAVE) (Lin et al. 2008), the large-scale, unstructured two-dimensional Advanced Circulation (2D ADCIRC) hydrodynamic model (http://www.adcirc.org), and the regional scale models, Curvilinear Hydrodynamics in three dimensions-Multi-Block (CH3D-MB) (Luong and Chapman 2009), which is the multi-block (MB) version of Curvilinear Hydrodynamics in three-dimensions-Waterways Experiments Station (CH3D-WES) (Chapman et al. 1996, Chapman et al. 2009), MB CH3D-SEDZLJ sediment transport model (Hayter et al. 2012), and CE-QUAL Management - ICM water quality model (Bunch et al. 2003, Cerco and Cole 1994). Task 1 of the DOER project, “Modeling Transport in Wetting/Drying and Vegetated Regions,” is to implement and test three-dimensional (3D) wetting and drying (W/D) within GSMB. This technical note describes the methods and results of Task 1. The original W/D routines were restricted to a single vertical layer or depth-averaged simulations. In order to retain the required 3D or multi-layer capability of MB-CH3D, a multi-block version with variable block layers was developed (Chapman and Luong 2009). This approach requires a combination of grid decomposition, MB, and Message Passing Interface (MPI) communication (Snir et al. 1998). The MB single layer W/D has demonstrated itself as an effective tool in hyper-tide environments, such as Cook Inlet, Alaska (Hayter et al. 2012). The code modifications, implementation, and testing of a fully 3D W/D are described in the following sections of this technical note.


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