DYNAMIC ANALYSIS OF FRAMES WITH MATERIAL AND GEOMETRIC NONLINEARITIES BASED ON THE SEMIRIGID TECHNIQUE

2008 ◽  
Vol 08 (03) ◽  
pp. 415-438 ◽  
Author(s):  
F. T. K. AU ◽  
Z. H. YAN
Keyword(s):  
Dynamic Analysis ◽  
Stiffness Matrix ◽  
Plastic Hinge ◽  
Nonlinear Dynamic Analysis ◽  
Yield Condition ◽  
Computationally Efficient ◽  
Time Step ◽  
Geometric Nonlinearities ◽  
Frame Element ◽  
Sum Of Products

This paper presents a method for nonlinear dynamic analysis of frames with material and geometric nonlinearities which is based on the semirigid technique. The plastic hinge that accounts for the material nonlinearity is modeled as a pseudo-semirigid connection with nonlinear hysteretic moment-curvature characteristics at the element ends. The stiffness matrix of a frame element with material and geometric nonlinearities is expressed as the sum of products of the standard stiffness matrix and the geometric stiffness matrix of the element, with their corresponding correction matrices based on the plasticity factors developed from the section flexural stiffness at the plastic hinge locations. The combined stress yield condition is used for the force state determination of plastic hinges, and force equilibrium iterations and geometry updating for frames are carried out in every time step. When the key parameters of a structure are updated in a time step, the time step is split up into substeps to ensure accuracy while keeping the computations to a reasonable amount. The plastic rotation history can be calculated directly or in an approximate indirect way. The method is computationally efficient and it needs no additional connection elements, which makes it convenient for incorporation into existing linear dynamic analysis programs. Besides, the method can handle accurately and efficiently the dynamic analysis of nonlinear frames using relatively large time steps in conjunction with time step subdivision to cope with key parameter changes. A portal frame is used to verify the correctness of the proposed method. A more complicated five-story frame is used to illustrate the applicability and performance of the proposed method.

scholarly journals Wavelet-based Decomposition of Ground Acceleration for Efficient Calculation of Seismic Response in Elastoplastic Structures

2020 ◽  
Author(s):  
Reza Kamgar ◽  
Noorollah Majidi ◽  
Ali Heidari
Keyword(s):  
Wavelet Transform ◽  
Dynamic Analysis ◽  
Continuous Wavelet Transform ◽  
Nonlinear Dynamic ◽  
Nonlinear Dynamic Analysis ◽  
Continuous Wavelet ◽  
Frequency Content ◽  
Time Step ◽  
Integration Schemes ◽  
The Waves

The nonlinear dynamic analysis provides a more accurate simulation of the structural behavior against earthquakes. On the other hand, this analysis method is time-consuming since the time-step integration schemes are used to calculate the responses of the structure. Wavelet transform is also considered as one of the strong computing tools in studying the properties of the waves. The continuous wavelet transform is a time-frequency study and examines the frequency content of the waves while, the discrete wavelet transform is used to reduce sampling data and also to eliminate the noise of the waves. In this paper, the discrete and continuous wavelet transforms are used to reduce the wave sampling and therefore to reduce the required time for analysis. In this regard, eight near- and far- field earthquakes are studied. The frequency content of the earthquake is investigated by the Fourier spectrum and the continuous wavelet transform. The results show that the first five frequencies for the main earthquakes are similar to those values of earthquakes obtained by wavelet transform. Besides, it is shown that using wavelet transform for the main and decomposed earthquakes indicates that the duration of strong ground motion and the time of dominant frequency occur approximately in the same domain. Finally, it is concluded that the required calculation time reduces to about 80 % with an error less than 6 % when the main earthquake is decomposed by wavelet transform and the approximation waves are used in the nonlinear dynamic analysis.

Geometric Nonlinear Dynamic Analysis of Tapered Steel Members

2020 ◽  
Author(s):  
Yasir F. Al-Lebban
Keyword(s):  
Dynamic Analysis ◽  
Mass Matrix ◽  
Nonlinear Dynamic Analysis ◽  
Axial Deformation ◽  
Step Size ◽  
Time Step ◽  
Time Step Size ◽  
Geometric Nonlinear ◽  
Steel Members ◽  
Mass Matrices

In this study, a theoretical analysis is presented for estimating the in-plane geometric nonlinear elastic stability behavior of steel members with tapered elements under dynamic loads. Beam-column approach is adopted for modeling the structural members as beam-column elements. The formulation is based on the Eulerian description taking into consideration the influence of axial force on bending stiffness. The changes in member chord length due to axial deformation and flexural bowing are also considered. In the dynamic analysis, the system mass properties have been represented using both lumped and consistent mass matrices. The consistent mass matrix is derived in three components: translational, rotational, and axial inertia. The formulation of the mass matrices in local and global coordinate systems of tapered members, which incorporates geometric nonlinearity, has been presented. A parametric study is conducted to examine the effects of number of tapered elements, tapering the prismatic members, time step size, and tapering ratio.

Masonry Spires: 3D Models to Understand their Seismic Vulnerability

2019 ◽  
Vol 817 ◽  
pp. 317-324
Author(s):  
Elena Zanazzi ◽  
Eva Coïsson ◽  
Daniele Ferretti ◽  
Alessio Lorenzelli
Keyword(s):  
Dynamic Analysis ◽  
Seismic Vulnerability ◽  
Linear Time ◽  
Numerical Models ◽  
Nonlinear Dynamic Analysis ◽  
Nonlinear Static Analysis ◽  
Time Step ◽  
Epicentral Area ◽  
Finite Element Software ◽  
Bell Tower

The May 2012 Emilia earthquake has highlighted the important vulnerability of masonry spires at the top of bell towers of churches. Indeed, almost half of those in the epicentral area have shown a typical damage mechanism consisting in the shear sliding and overturning of the top of the spire. Given the recurrence of this phenomenon, the present paper tries to provide a contribution to the comprehension of the seismic behaviour of the spires through the numerical analysis of three case studies. In particular, the work analyses the spires of the churches of San Nicola di Bari in Cortile, near Carpi (MO); Sant'Egidio in Cavezzo (MO), and Sant'Agostino in Sant'Agostino (FE). The numerical models of these masonry structures were made using Abaqus Finite Element software. After the creation of the three-dimensional geometric models, a first nonlinear static analysis of the entire bell tower was performed adopting for masonry the Abaqus “concrete damage plasticity model”. Once the stability of the bell tower was verified for dead loads, the non-linear time-step dynamic analysis was faced. This required the definition of the seismic input at the base of the tower, through the accelerograms recorded by the closest stations. The nonlinear dynamic analysis of the global model of the bell tower provided the floor response spectra at the base and at the top of the spire. Indeed the comparison between spectra at the ground and at the top highlights the filter effect of the stem of the bell tower with a significant increase in accelerations at the top. This effect may explain the widespread damage observed at the top of the spires. Eventually, three different non-invasive intervention techniques were proposed in compliance with the principles of restoration and were modelled to compare their behaviour.

A Nonlinear Dynamic Substructuring Approach to Global Dynamics of Flexible Riser Systems

2014 ◽  
Author(s):  
Arya Majed ◽  
Phil Cooper
Keyword(s):  
Dynamic Analysis ◽  
Nonlinear Dynamic ◽  
Nonlinear Dynamic Analysis ◽  
Nonlinear Effects ◽  
Global Dynamics ◽  
Computationally Efficient ◽  
Flexible Riser ◽  
Dynamic Simulations ◽  
Stick Slip ◽  
Global Dynamic

Standard riser global dynamic analysis software packages utilize line element models that cannot capture the complex behavior of flexible risers. This paper presents a computationally efficient nonlinear dynamic analysis methodology capable of incorporating detailed finite element models and scalable to global dynamic simulations of entire flexible riser systems. Subject methodology captures the global geometric nonlinear effects and its coupling to stick-slip friction — a clear requirement for accurate armour stress predictions. In addition, the method enables the formulation of stress transformation matrices which allow the direct recovery of armour stresses from the global simulations. A demonstration problem involving the nonlinear dynamic simulation of a 500m flexible riser system is presented.

Inelastic Dynamic Analysis of Steel Structure Using Force Analogy Method

2012 ◽  
Vol 166-169 ◽  
pp. 304-309 ◽  
Author(s):  
Shi Qiang Song ◽  
Gang Li
Keyword(s):  
Dynamic Analysis ◽  
Plastic Hinge ◽  
Nonlinear Dynamic Analysis ◽  
Steel Structure ◽  
Response Analysis ◽  
Analysis Method ◽  
Element Analysis ◽  
Analogy Method ◽  
Traditional Algorithm ◽  
Response State

Force analogy method is a kind of nonlinear dynamic analysis method. Analyzing inelastic structural behavior by using plastic hinge theory, it is widely appropriate to many structures with different material properties and very time efficient and numerically accurate without complicated iterative computations in traditional algorithm. Compared with the traditional finite-element analysis method, dynamic response analysis based on force analogy method has obvious advantages. The application of force analogy method to a steel structure is presented and the analysis result shows that the method algorithm can represent each response state of the structure in real-time and has the very good accuracy and practical.

scholarly journals Practical Aspects Concerning Nonlinear Dynamic Analysis of Cable Structures

2013 ◽  
Vol 9 (3) ◽  
pp. 25-31
Author(s):  
Ferencz Lazar-Mand
Keyword(s):  
Dynamic Analysis ◽  
Nonlinear Dynamic ◽  
Stiffness Matrix ◽  
Nonlinear Dynamic Analysis ◽  
Linear Matrix ◽  
Tangent Stiffness Matrix ◽  
Cable Structure ◽  
Cable Structures ◽  
Constant Stiffness ◽  
Non Linear

Abstract The paper is about some aspects concerning the nonlinear dynamic analysis of prestressed cable structures. A method for the assessment of the tangent stiffness matrix and of the nonlinear parameters is proposed. The methodology is similar to the one described by P. Krishna. The Newmark method is used to integrate the motion equation. In the final section of the paper a comparison between the output supplied by the software of the presented method is made, with constant stiffness matrix(linear) and with the non-linear matrix updated step by step (geometric non-linear). The elements used for comparison are the displacement and velocity response of a given pretensioned cable structure.

A New Procedure for Nonlinear Dynamic Analysis of Structures Under Seismic Loading Based on Equivalent Nodal Secant Stiffness

2018 ◽  
Vol 18 (03) ◽  
pp. 1850043 ◽  
Author(s):  
Tzu-Ying Lee ◽  
Kun-Jun Chung ◽  
Hao Chang
Keyword(s):  
Dynamic Analysis ◽  
Nonlinear Dynamic Analysis ◽  
Seismic Loading ◽  
Analysis Procedure ◽  
Structural Systems ◽  
Equilibrium Equations ◽  
Lumped Mass ◽  
Time Step ◽  
Highly Nonlinear ◽  
Secant Stiffness

This paper presents a dynamic analysis procedure for predicting the responses of large, highly nonlinear, discontinuous structural systems subjected to seismic loading. The concept of equivalent nodal secant stiffness is adopted to diagonalize the conventional stiffness matrix of the structure. With the lumped-mass idealization, the decoupled equilibrium equations of the structure are then solved by the implicit Newmark integration method. Additionally, an incremental-iterative procedure is performed to ensure that the equilibrium conditions are satisfied at the end of each time step. The proposed analysis procedure has the advantages of both the conventional explicit and implicit integration procedures, but with their disadvantages removed. Through extensive applications, the results demonstrate that the proposed procedure is simple and robust for analyzing practical structural systems in terms of computational efficiency and stability.

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