Temperature Analysis of Pin-Jointed Spherical Domes

1988 ◽  
Vol 3 (4) ◽  
pp. 217-220
Author(s):  
Zs. Gáspár
Keyword(s):  
Stiffness Matrix ◽  
Angular Diameter ◽  
Spherical Coordinates ◽  
Temperature Analysis ◽  
Spherical Dome ◽  
Load Vector ◽  
Uniform Change

The stiffness matrix of a pin-jointed spherical dome is expressed in spherical coordinates and the load vector is derived for uniform change of temperature. This method of representation may be used when improving the best available estimates of the Tammes problem (How must n equal, non-overlapping circles be packed on a sphere so that the angular diameter of the circles will be as great as possible?).

Spectral Analysis of Deteriorated Offshore Structures

2007 ◽  
Author(s):  
H. Karadeniz
Keyword(s):  
Failure Mechanism ◽  
Stiffness Matrix ◽  
Progressive Failure ◽  
Offshore Structures ◽  
Mode Shapes ◽  
Solution Technique ◽  
Random Load ◽  
Practical Applications ◽  
Mass Matrices ◽  
Load Vector

In order to present an efficient, practical technique to determine progressive failure mechanism of structures, modelling of member deterioration by using a spring system is outlined. The procedure uses updates of member stiffness and mass matrices as well as the random load vector in incremental forms. In this procedure, the assembly process produces redistributions of the system stiffness and mass matrices, and the load vector. In the calculation of response spectral values, the original forms remain unchanged. Inversion of the stiffness matrix is calculated by using the Neumann expansion solution in which the original stiffness matrix is inverted only once so that a considerable computation time is saved in the whole calculation process. An incremental solution technique is presented for spectral analyses of both static and dynamic sensitive structures. In the case of dynamic analysis, special attention is paid to estimations of modified natural frequencies and mode shapes of deteriorated structures, which may affect response spectral values considerably. The technique, which is presented in the paper, is attractive in practical applications and can be efficiently used in the reliability calculation as well, and also it can be successfully used to determine a progressive failure mechanism of the structure.

A simple and efficient method for introducing faults into finite element computations

1981 ◽  
Vol 71 (5) ◽  
pp. 1391-1400
Author(s):  
H. J. Melosh ◽  
A. Raefsky
Keyword(s):  
Finite Element ◽  
Stiffness Matrix ◽  
Degrees Of Freedom ◽  
Displacement Discontinuity ◽  
Element Level ◽  
Single Node ◽  
Node Point ◽  
Local Element ◽  
Great Utility ◽  
Load Vector

abstract This paper outlines a new method, the “split node technique” for introducing fault displacements into finite element numerical computations. The value of the displacement at a single node point shared between two elements depends upon which element it is referred to, thus introducing a displacement discontinuity between the two elements. We show that the modification induced by this splitting can be contained in the load vector, so that the stiffness matrix is not altered. The number of degrees of freedom is not increased by splitting. This method can be implemented entirely on the local element level, and we show rigorously that no net forces or moments are induced on the finite element grid when isoparametric elements are used. This method is thus of great utility in many geological and engineering applications.

scholarly journals Linear Analysis of Stability of Pitched Roof Frames

2018 ◽  
Vol 12 (1) ◽  
pp. 282-295
Author(s):  
T. Mariano Bocovo ◽  
Gerard Gbaguidi Aisse ◽  
Gerard Degan
Keyword(s):  
Stiffness Matrix ◽  
Displacement Vector ◽  
Stability Functions ◽  
Four Frames ◽  
Arch Effect ◽  
Sign Change ◽  
Load Vector ◽  
Analysis Of Stability ◽  
The Stability ◽  
Geometric Nonlinear Analysis

Background: In this paper, geometric nonlinear analysis of pitched roof frames was carried out by the stiffness matrix method using stability functions. Objective: This study contributes to a better knowledge of the stability of pitched roof frames, not braced, and therefore of the efficiency in their dimensioning. Method: At first, the argument of the stability functions was set as 0.01. The stiffness matrix of the frame has been assembled, as well as the nodal load vector of the frame. The boundary conditions (support restraint and wind bracing restraint) were introduced for the reduction of this matrix and the nodal load vector. At this stage, the determinant of the reduced stiffness matrix and the reduced nodal displacement vector are calculated. The argument of the stability functions is incremented by 0.01 and the operations are repeated until the determinant of the reduced stiffness matrix changes sign. The argument of the iteration preceding the sign change of the determinant and corresponding to its positive value is taken and refined by a process described in the paper. The buckling loads of the frame members are determined at this stage. Results and Conclusion: The analysis focused on four frames; the obtained results show that the increase in the inclination of the crossbar makes it possible to take full advantage of the “arch effect”. Arch effect is due to the presence of crossbars which have a linear arch shape. Furthermore, the angle as well as the length ratio, between the crossbar and post, influence critical load value.

scholarly journals Influence of Anchor Connector Stiffness on Displacement-Internal Force of Steel-Concrete Frame

2019 ◽  
Vol 8 (2) ◽  
pp. 3614-3619
Keyword(s):  
Structural Steel ◽  
Stiffness Matrix ◽  
Composite Beam ◽  
Concrete Beam ◽  
Internal Force ◽  
Beam Element ◽  
Steel Frame ◽  
Concrete Frame ◽  
Load Vector ◽  
The Impact

In the article, the author introduces how to determine the equivalent hardness of steel-concrete composite beam element, stiffness matrix and nodal load vector of steel-concrete beam element. Thereby, to build and solve the problem of analyzing the structural steel frame of concrete considering the anchor stiffness, programming and clarifying the impact of anchor stiffness associated with displacement - internal force of the frame

scholarly journals Building the Stiffness Matrix and Load Vector of the Taper Elements with the I-Section that Considering the Effect of Shear Force and Stiffness of the Connection

2019 ◽  
Vol 8 (2) ◽  
pp. 3633-3641
Keyword(s):  
Mathematical Model ◽  
Structural Analysis ◽  
Energy Method ◽  
Stiffness Matrix ◽  
Shear Force ◽  
Analysis Program ◽  
Analysis Problem ◽  
Rigid Connection ◽  
Load Vector

This paper shows how to build stiffness matrix and load vector by energy method for taper, I section elements includes the effects of shear and semi-rigid connection, use for structural analysis problem. Mathematical model of the section is exponential. Thereby, programming the structural analysis program for taper elements and verify results stiffness matrix, load vector as well as assessing the effects of shear and semi-rigid connection to force and displacement of this element

Modeling of Externally Prestressed Beams until Fracture in Non Linear Elasticity

2015 ◽  
Vol 749 ◽  
pp. 379-385 ◽  
Author(s):  
Arezki Adjrad ◽  
Youcef Bouafia ◽  
Mohand Said Kachi ◽  
Hélène Dumontet
Keyword(s):  
Linear Elasticity ◽  
Prestressed Concrete ◽  
Stiffness Matrix ◽  
Axial Load ◽  
Concrete Beams ◽  
Transverse Component ◽  
System Of Equations ◽  
Non Linear ◽  
Load Vector ◽  
Prestressed Beams

In this paper, we present an analytical model to analyze reinforced and prestressed concrete beams loaded in combined bending, axial load and shear, in the frame of non linear elasticity. In this model, the equilibrium of the beam is expressed by solving a system of equations, governing beams equilibrium, based on the stiffness matrix of the beam, which connects the load vector to the node displacements vector of the beam. It is built from the stiffness matrix of the section which takes into account a variation of the shearing modulus (depending on the shear variation) instead of assuming a constant shearing modulus as in linear elasticity. For the internal tendons, the stiffness matrix is completed by the terms due to the prestress effect in flexural equilibrium and by the balancing of one part of the shear by the transverse component of the force in the inclined cables.

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