Study of the Analysis Methods of Wave-Passage Effect Based on ABAQUS

Advanced Materials Research Vols 163-167 (2011) pp 4316-4319 © (2011) Trans Tech Publications, Switzerland doi:10.4028/www.scientific.net/AMR.163-167.4316

Online: 2010-12-06

Study of the Analysis Methods of Wave-Passage Effect Based on ABAQUS Jueyang Zhang1, a, Zaigen Mu1, b and Ming Gan2 1

University of Science and Technology T echnology Beijing, Beijing 100083, China 2

Beijing Institute of Architecture Design, Beijing 100045, China a

b

[email protected], [email protected]

Keywords: W Keywords: Wave-Passage ave-Passage Effect; Large Mass Method; Acceleration Method; ABAQUS.

Abstract. wave-passage effect of the seismic is the main reason of multi-support excitations, and there are always two analysis analysis methods which are large mass method and acceleration metho d to study on the multi-support excitations, this paper take one kind of trussed structure as an example, use the two methods to consider the wave-passage effect of seismic, compare the difference between the results from using the two methods, and also compare the difference between single-support and multi-support excitations. This paper draw a conclusion that it is a precise way to using ABAQUS to analysis the wave-passage effect of the seismic; wave-passage effect of the seismic has an great influence on the reaction of long-span spatial structures, it must be considered in the similar projects; and the large method and acceleration method both have their advantages and disadvantages, so we should give concrete analysis to concrete problems. Introduction

The ground motion is a complicated time-space process. There are some characters about the seismic in the process of propagation, such as incoherence effect, wave-passage effect, site-response effect and attenuation affect etc. It has been verified that the ground motions inputting at different supports of long-span structures are different, which may be modeled by phase shifts and coherency losses. The phase shifts are caused cau sed by waves propagating, while the coherency loses can be attributed to many factors such as source mechanism, path and local site effects, etc. Significant contributions on these issues have been made, and studies on response of long span structures have shown that the effects of multi-support excitations must be considered. There usually two ways in conducting multi-point analysis. First, acceleration method, that is, giving direct excitations to the basis of the structure. Second, the large mass method, that is, adding a large mass to the nodes which need exerting acceleration boundary conditions, as the point mass is greater than structure’s, the point mass and the concentration force can give precise acceleration boundary conditions to the structure. s tructure. Theoretical Theoretical analysis of the acceleration acceleration method

The reaction of the structure comes from two parts : one is the reaction of the t he bearing moving called the quasi-static response; the other is inertial forces to the structure caused by the acceleration of bearing moving, called dynamic response, that is : u s  u ss  usd  (1)   =  s  +   u u  b  b   0  ，

d

Where u s is the dynamic displacement component

s

，

u s is the quasi-static displacement

component: u s s = rsbubs

(2)

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Advanced Materials Research Vols. 163-167

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The dynamic equilibrium equation of the Multi-point excitation is that:   ss u s + Cssu s + K ssu s = −K sbu b (3) Combine the Eq.(1) (2) (3) the dynamic equilibrium equation of the structure is identical to: d d d s s s      (4) ss u s + C ssu s + K ssu s = −M ssu s − C ssu s − C sbu b ，

，

，

The right side of the equation is the equivalent effective point force damping force is negligible in terms of inertial force and taking into account of the Eq.(2) another equation can be found: ，

，

，

u + C u + K ssu = −M r u

d  ss s

d  ss s

d s

s  ss sb b

(5) Theoretical Theoretical analysis of the large l arge mass method

The large mass method, that is, adding a large mass to the nodes which need exerting acceleration boundary conditions, and exerting a concentration force P which P which is the same direction to the seismic excitation, then: P = M 0 {u0 } (6) In Eq.(6),

0

is the large mass; u0 is the acceleration excitation, substitute

0

, P into P into the

dynamic equilibrium equation: m j1u1 +  + M 0uj +  + m jnun + c j 1u1 +  + c jju j +  + c jnun + k j1u1 +  + k jnun = M 0u0 Both of the side of the equation Divided by

0

(7)

, because M 0 is much larger than m , it can be

considered u j ≈ u0 . Finite element analysis

On multi-input study, set up the 3D model mod el of a trussed structure in i n ABAQUS analyze the regularity of torsion effect of the structure under the two methods, and compare the advantages and disadvantages of the two methods. The calculation model is shown in Fig. 1. In the calculation model, the travelling velocity is 250m/s, the seismic wave is El. centro wave, compare the different results of using the two methods by studying the point A’s displacement time history curve. ，



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Advances in Structures

requires solving large linear equations. so the process need to take up a considerable amount of com puting resources, disk space and memory, Incremental step of this algorithm must be relatively big, at least bigger than the explicit algorithm, but in the actual computations, it depends on the number of iterations and the nonlinear degree, so the incremental step need to take a reasonable value. Large mass method in ABAQUS. In ABAQUS, the large mass method is through using a co mmand stream: BASE MOTION, to consider the sub-base, then do multi-support excitations, it is an explicit algorithm. In order to distinguish the difference among them, the results of the above two methods for multisupport excitation excitatio n and single-support excitation excitati on are as shown in Fig. 2 in the same coordinate system.

Fig. 2 U1 displacement time history analysis curve under large mass method, acceleration method and single-support excitation In Fig. 2, it can be found that no matter the large method or acceleration method, the displacement response is larger than the response of single-support excitation. And the results from large mass method and the acceleration method are almost the same, only a little deviation. So in conclusion, both the two methods can be used in multi-support excitation. However, the large mass method’s accuracy is mostly depends on the size of the additional mass, if a little smaller, the results obtained will be errors, while if a little larger, it will result in data overflow error. Usually, in order to get six decimal places of accuracy, the value of each additional mass should be 106 times larger than the structure’s, and also the rotational inertia should be taken as 106 times larger than the structure’s. Conclusion

This paper describes the method of studying multi-support excitation, and by using ABAQUS to compare the large mass method and acceleration method, and also compare them to the result from single-support excitation. There are some conclusions as follows: ● ●

●

The response from multi-support excitation is bigger than that from single-support excitation. The result by using large mass method or acceleration method is almost the same, so they can both be used in multi-support mult i-support excitation excitat ion analysis. In ABAQUS, the large mass method is carried out by implicit algorithm, it need to solve



Advanced Materials Research Vols. 163-167

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algorithm, it does not need to solve a large number of equations, the speed of the solver is fast, and it has accumulated errors.

Acknowledgment

The authors gratefully acknowledge support from the National Natural Science Foundation of China through grant 50878022. This work is also supported by the grant 8082017 from the Beijing Municipal Natural Natural Science Science Foundatio Foundation. n. References

[1] Wilson E, et al: A Clarification of the Orthogonal Effects in A three-dimensional Seismic Analysis Earthquake Spectra, Vol.11, No. 4, pp. 659~666,1995. [2] Todorovska M I and Trifunac M D: Response spectra for differential motion of columns[M/CD]. Auckland: Elsevier Science Ltd, 12th WCEE, 2000. [3] Hao H. and Duan X.N.: Seismic response of asymmetric structures to multiple ground motions. Journal of Structural Engineering, Vol.121, No.11, pp. 1557~1564, 1995. [4] Kemal Hacıefendioğlu, Alemdar Bayraktar and Yasemin Bilici: The effects of ice cover on stochastic response of concrete gravity dams to multi-support seismic excitation, Cold Regions Science and Technology, Vol. 55, pp. 295~ 295~303, 2009.



Advances in Structures

10.4028/www.scientific.net/AMR.163-167

Study of the Analysis Methods of Wave-Passage Effect Based on ABAQUS

10.4028/www.scientific.net/AMR.163-167.4316 DOI References

[3] Hao H. and Duan X.N.: Seismic response of asymmetric structures to multiple ground motions. ournal of Structural Engineering, Vol.121, No.11, pp. 1557~1564, 1995. doi:10.1061/(ASCE)0733-9445(1995)121:11(1557) [3] Hao H. and Duan X.N.: Seismic response of asymmetric structures to multiple ground motions. Journal of Structural Engineering, Vol.121, No.11, pp. 1557~1564, 1995. doi:10.1061/(ASCE)0733-9445(1995)121:11(1557)

Study of the Analysis Methods of Wave-Passage Effect Based on ABAQUS

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