Application of the Direct Stiffness Method to Plane Problems Involving Large, Time-Dependent Deformations

1966 ◽  
Vol 88 (4) ◽  
pp. 771-776 ◽  
Author(s):  
G. F. Gerstenkorn ◽  
A. S. Kobayashi
Keyword(s):  
Large Time ◽  
Numerical Procedure ◽  
Structural Response ◽  
Small Time ◽  
Time Dependent ◽  
Polar Coordinates ◽  
Structural Problems ◽  
Stiffness Method ◽  
Direct Stiffness ◽  
Creep Deformations

The direct stiffness method is used to formulate a numerical procedure for solving plane structural problems involving large, time-dependent deformations and nonhomogeneous, time-dependent material properties. The stiffness matrix in polar coordinates is derived for the state of plane strain. The nonlinear structural response is incrementally linearized by considering the deformation process to be linear within small time increments. The developed procedure is compared numerically with a known solution of creep deformations in a thick-walled cylinder subjected to internal pressure loading and elevated temperature.

Structural Analysis of an Arteriole by the Direct Stiffness Method

1966 ◽  
Vol 88 (4) ◽  
pp. 363-368 ◽  
Author(s):  
G. F. Gerstenkorn ◽  
A. S. Kobayashi ◽  
C. A. Wiederhielm ◽  
R. F. Rushmer
Keyword(s):  
Structural Analysis ◽  
Cross Section ◽  
Piecewise Linear ◽  
Structural Response ◽  
Polar Coordinates ◽  
Heterogeneous Structure ◽  
Time Data ◽  
Stiffness Method ◽  
Direct Stiffness ◽  
The Cross

The direct stiffness method is used to analyze the structural response of the cross section of an arteriole which is both heterogeneous and nonlinear in terms of structural response. A typical segment of the cross section is represented by an assembly of triangular elements. The stiffness matrix and strain-displacement relationships are then derived in terms of polar coordinates for a triangular plate element. Viscoelasticity is included in this structural analysis by using a piecewise linear approach. Stress-time and displacement-time data are presented for two typical cross sections of the arteriole. These results reveal special properties of a heterogeneous structure which is undergoing viscoelastic deformations.

Numerical Modelling of Time-Dependent Behaviour of Reinforced Concrete Structure with Use of B3 Model

2014 ◽  
Vol 14 (2) ◽  
pp. 38-45
Author(s):  
Jiří Koktan ◽  
Jiří Brožovský
Keyword(s):  
Reinforced Concrete ◽  
Time Dependent ◽  
Technical Standard ◽  
Reinforced Concrete Structure ◽  
Concrete Frames ◽  
Creep Analysis ◽  
Stiffness Method ◽  
Direct Stiffness ◽  
Time Dependent Behaviour ◽  
Dependent Behaviour

Abstract The paper proposes an implementation of creep analysis of reinforced concrete structures which utilizes the B3 model and the direct stiffness method for reinforced concrete frames. The analysis is based on a numerical integration and it is implemented in an algorithmic programming language. There is presented a solution with the mentioned approaches which is compared with solution based on the EN 1992-1-1 technical standard.

scholarly journals Large Time Decay of Solutions to a Linear Nonautonomous System in Exterior Domains

Mathematics ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 841
Author(s):  
Toshiaki Hishida
Keyword(s):  
Evolution Operator ◽  
Large Time ◽  
Rigid Motion ◽  
Time Dependent ◽  
Energy Relation ◽  
Exterior Domains ◽  
Decay Properties ◽  
Decay Of Solutions ◽  
Whole Space ◽  
Expository Paper

In this expository paper, we study Lq-Lr decay estimates of the evolution operator generated by a perturbed Stokes system in n-dimensional exterior domains when the coefficients are time-dependent and can be unbounded at spatial infinity. By following the approach developed by the present author for the physically relevant case where the rigid motion of the obstacle is time-dependent, we clarify that some decay properties of solutions to the same system in whole space Rn together with the energy relation imply the desired estimates in exterior domains provided n≥3.

Comment on "Basis for Derivation of Matrices for the Direct Stiffness Method"

AIAA Journal ◽  
1964 ◽  
Vol 2 (6) ◽  
pp. 1161-1161
Author(s):  
E. L. COOK ◽  
R. E. CHAPEL ◽  
W. D. BERNHART
Keyword(s):  
Stiffness Method ◽  
Direct Stiffness

On the Control of Chaos in Extended Structures

1997 ◽  
Vol 119 (4) ◽  
pp. 551-556 ◽  
Author(s):  
C. Barratt
Keyword(s):  
Nearest Neighbor ◽  
Duffing Oscillator ◽  
Vertical Plane ◽  
Small Time ◽  
Time Dependent ◽  
External Forcing ◽  
Control Of Chaos ◽  
Chaotic Vibrations ◽  
Order Of Magnitude ◽  
The Individual

A mechanism is proposed for synchronizing the chaotic vibrations of an externally forced array of oscillators with nearest-neighbor viscoelastic coupling. The proposed mechanism involves the application of small time-dependent perturbations to the individual oscillators. The perturbations required to preserve the coherence are of the order of magnitude of any noise present. The mechanism works with any form of external forcing. A modification of the mechanism is used to control the forced chaotic vibrations of a single Duffing oscillator allowed to vibrate out of the vertical plane.

Infrastructure Sustainability

2011 ◽  
pp. 202-211
Author(s):  
Praveen Moragaspitiya ◽  
David Thambiratnam ◽  
Nimal Perera ◽  
Tommy Chan
Keyword(s):  
Numerical Procedure ◽  
Time Dependent ◽  
Test Procedures ◽  
High Rise ◽  
Secondary Systems ◽  
Content Variable ◽  
True Time ◽  
And Performance ◽  
Concrete Elements ◽  
Axial Shortening

High density development has been seen as a contribution to sustainable development. However, a number of engineering issues play a crucial role in the sustainable construction of high rise buildings. Non linear deformation of concrete has an adverse impact on high-rise buildings with complex geometries, due to differential axial shortening. These adverse effects are caused by time dependent behaviour resulting in volume change known as ‘shrinkage’, ‘creep’ and ‘elastic’ deformation. These three phenomena govern the behaviour and performance of all concrete elements, during and after construction. Reinforcement content, variable concrete modulus, volume to surface area ratio of the elements, environmental conditions, and construction quality and sequence influence on the performance of concrete elements and differential axial shortening will occur in all structural systems. Its detrimental effects escalate with increasing height and non vertical load paths resulting from geometric complexity. The magnitude of these effects has a significant impact on building envelopes, building services, secondary systems, and lifetime serviceability and performance. Analytical and test procedures available to quantify the magnitude of these effects are limited to a very few parameters and are not adequately rigorous to capture the complexity of true time dependent material response. With this in mind, a research project has been undertaken to develop an accurate numerical procedure to quantify the differential axial shortening of structural elements. The procedure has been successfully applied to quantify the differential axial shortening of a high rise building, and the important capabilities available in the procedure have been discussed. A new practical concept, based on the variation of vibration characteristic of structure during and after construction and used to quantify the axial shortening and assess the performance of structure, is presented.

Small‐time, large‐time, and asymptotics for the Rough Heston model

2020 ◽  
Author(s):  
Martin Forde ◽  
Stefan Gerhold ◽  
Benjamin Smith
Keyword(s):  
Large Time ◽  
Small Time ◽  
Heston Model
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