Rigid-body displacements of curved elements in the analysis of shells by the matrix- displacement method.

AIAA Journal ◽  
1967 ◽  
Vol 5 (8) ◽  
pp. 1525-1527 ◽  
Author(s):  
WALTER E. HAISLER ◽  
JAMES A. STRICKLIN
Keyword(s):  
Rigid Body ◽  
Displacement Method ◽  
The Matrix ◽  
Curved Elements

Study of the Influence of the Beam-Column Line Stiffness Ratio on the Frame Structure Load Capacity Based on MATLAB

2011 ◽  
Vol 71-78 ◽  
pp. 4194-4198
Author(s):  
Shao Qin Zhang ◽  
Hua Hu Cheng
Keyword(s):  
Engineering Design ◽  
Carrying Capacity ◽  
Calculated Result ◽  
Load Capacity ◽  
Frame Structure ◽  
Stiffness Ratio ◽  
Displacement Method ◽  
Structure Form ◽  
The Matrix ◽  
Internal Forces

Statically indeterminate frame, composed of beams and columns, is a widely used structure form in civil engineering. The frame carrying capacity under various actions is related to the absolute stiffness of frame components and relative beam-column line stiffness ratio. The matrix displacement method and programming based on MATLAB were employed in this study to calculate the internal forces and displacements of a 2-bay 2-story frame structure under the action of horizontal loads. The influence of the beam-column line stiffness ratio on the frame load capacity was discussed based on the calculated result. Furthermore some advises were provided about the reasonable beam-column line stiffness ratio for engineering design.

A Sequel to Technical Note 13: The Curved Tetrahedronal and Triangular Elements TEC and TRIC for the Matrix Displacement Method

1969 ◽  
Vol 73 (697) ◽  
pp. 55-65 ◽  
Author(s):  
J. H. Argyris ◽  
D. W. Scharpf
Keyword(s):  
Computational Analysis ◽  
Three Dimensional ◽  
Technical Note ◽  
Radius Of Curvature ◽  
Two Dimensional ◽  
Displacement Method ◽  
Stress Concentrations ◽  
The Past ◽  
The Matrix ◽  
Triangular Elements

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.

The Hermes 8 Element for the Matrix Displacement Method

1968 ◽  
Vol 72 (691) ◽  
pp. 613-617 ◽  
Author(s):  
J. H. Argyris ◽  
I. Fried ◽  
D. W. Scharpf
Keyword(s):  
Dimensional Analysis ◽  
Three Dimensional ◽  
Displacement Method ◽  
The Matrix ◽  
Interpolation Techniques ◽  
Hermitian Interpolation

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.

The SHEBA Family of Shell Elements for the Matrix Displacement Method

1968 ◽  
Vol 72 (694) ◽  
pp. 873-883 ◽  
Author(s):  
J. H. Argyris ◽  
D. W. Scharpf
Keyword(s):  
Boundary Layer ◽  
Thin Shells ◽  
Displacement Method ◽  
Considerable Effort ◽  
Shell Elements ◽  
The Past ◽  
The Matrix ◽  
Specific Geometry

Considerable effort has been extended over the past years in adapting the matrix displacement method to the specific problems of thin shells under membrane and bending action and developing suitable elements of varying sophistication. Some of the difficulties arising in the process of idealisation were reviewed in ref. 1. For example, simple considerations show that a representation of a shell by polyhedron surfaces may lead to serious errors, especially in the presence of pronounced bending and so-called boundary-layer effects. For this and other reasons it appears imperative to allow for the curvature of the shell. Much ingenuity has been shown in evolving elements for shells of specific geometry.

scholarly journals From deep TLS validation to ensembles of atomic models built from elemental motions

2015 ◽  
Author(s):  
Alexandre Urzhumtsev ◽  
Pavel Afonine ◽  
Andrew H Van Benschoten ◽  
James Fraser ◽  
Paul D Adams
Keyword(s):  
Rigid Body ◽  
Diffraction Data ◽  
Harmonic Vibration ◽  
Mathematical Framework ◽  
Matrix Elements ◽  
Computational Tools ◽  
X Ray ◽  
Structural Ensembles ◽  
The Matrix ◽  
Rigid Body Motions

The widely used Translation Libration Screw (TLS) approximation describes concerted motions of atomic groups in X-ray refinement. TLS refinement often provides a better interpretation of diffraction data and the resulting rigid body motions may subsequently be assigned biochemical significance. In TLS refinement, three matrices (T, L and S) describe harmonic vibration, libration and their correlation. Because these matrices describe specific motions, they impose a number of conditions on their elements. Ignoring these conditions while refining the matrix elements may result in matrices that cannot be interpreted in terms of physically realistic motions. We describe a mathematical framework and the computational tools to analyze refined TLS matrices through their decomposition into descriptors of underlying motions. This allows for straightforward validation and identification of implausible TLS parameters. An algorithm for the generation of structural ensembles that are consistent with given TLS parameters, implemented as a part of the Phenix project, is also described.

scholarly journals Programming for solving plane rigid frame based on MATLAB

2020 ◽  
Vol 319 ◽  
pp. 09003
Author(s):  
Xiaokun Chen
Keyword(s):  
Computer Calculation ◽  
Bending Moment ◽  
Internal Force ◽  
Visual Design ◽  
Displacement Method ◽  
Whole Process ◽  
Programming Tool ◽  
Rigid Frame ◽  
The Matrix ◽  
Manual Calculation

Based on the idea of the matrix displacement method, this paper designs a program which can be used to solve the internal force of the continuous beam and rigid frame with MATLAB. It mainly demonstrates how to design a program to realize the matrix displacement method with MATLAB. In addition, some techniques are included in order to realize the correspondence between the manual calculation and the computer calculation, such as “Using lambda to locate”, “Crossing out rows and columns” and visual design. Therefore, based on the structural mechanics, combined with the principle of matrix displacement method, this paper shows the whole process from inputting the information of the rigid frame to solving the internal force of the rigid frame to outputting the bending moment diagram using MATLAB as the programming tool.

Tetrahedron Elements with Linearly Varying Strain for the Matrix Displacement Method

1965 ◽  
Vol 69 (660) ◽  
pp. 877-880 ◽  
Author(s):  
J. H. Arcyris,
Keyword(s):  
Three Dimensional ◽  
Technical Note ◽  
Considerable Improvement ◽  
Elastic Behaviour ◽  
Large Displacements ◽  
Two Dimensional ◽  
Displacement Method ◽  
The Matrix ◽  
Cardinal Point ◽  
Natural Strains

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.

A Tapered TRIM 6 Element for the Matrix Displacement Method

1966 ◽  
Vol 70 (671) ◽  
pp. 1040-1043 ◽  
Author(s):  
J. H. Argyris
Keyword(s):  
Displacement Method ◽  
Linear Type ◽  
Nodal Points ◽  
The Matrix ◽  
Triangular Elements ◽  
Important Extension ◽  
Special Case

The success achieved in wing analysis and related problems through the introduction of triangular elements with six nodal points and a prescribed linearly varying strain or stress, naturally raised demands for a further sophistication in the idealisation process by triangularisation. In this context a practically important extension is concerned with the influence of taper in the thickness. We reproduce in what follows the theory for the special case of linear type. The paper may be considered as a generalisation of notes 2 and 3 of this series. However, the analysis is here based on the non-dimensional homogeneous triangular co-ordinates introduced in note 5, which simplify the argument considerably. A significant broadening of the applicability of the new element will be given in notes 9 and 10.

The matrix displacement method

2019 ◽  
pp. 178-198
Author(s):  
John Bird ◽  
Carl Ross
Keyword(s):  
Displacement Method ◽  
The Matrix
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