ارائه روش هايپر المانهاي فشرده براي محاسبه توابع گرين در محيط هاي نامنظم هندسي

چكيده انگليسي :

Developing the Compacted Hyeprelements Method CHM for Calculation of Green s Functions in Irregular Media Sattar Dorafshan s dorafshan@cv iut ac ir Date of submission 26 06 2011 Department of Civil Engineering Isfahan University of Technology Isfahan 84156 83111 IranDegree M Sc Language FarsiSupervisor Farhad Behnamfar P hd Farhad@cc iut ac ir Abstract The main purpose of this thesis is to obtain numerical Green s functions for a laminated mediaconsisting of irregular boundaries subjected to Rayleigh waves The formulation of this problem isdeveloped on the basis of the thin layer method TLM Existing natural boundaries such as foundations faults etc which are definitely non vertical in soil shows the importance of developing irregular consistentboundaries In this research the stiffness matrix of the irregular boundary is constructed by using thestiffness matrix attributed to a vertical boundary by means of considering hypothetic degrees of freedomalong the depth of the stratum Then these degrees of freedom are accommodated within the originaldegrees of freedom of the bounded region by subdividing the zone limited at top to the non verticalboundary by a sufficient number of hyperelements Since the stiffness matrix for each hyperelement isavailable producing the total stiffness matrix for the irregular boundary region is straightforward Then applying a static condensation procedure to eliminate the hypothetic degrees of freedom the dynamicstiffness matrix of the nodes existing only on the irregular boundary is obtained Now the analysis of thebounded region with irregular boundaries is possible and if the forces or excitations are unit loads theresponses of the region will actually be the Green s functions for the region In the case of the seismicwaves two types of waves propagating in the earth are considered namely the Love waves with thedirection motion of particles perpendicular to the plane of propagation out of plane displacements and theRayleigh waves with the motion of particles taking place in the plane of propagation in planedisplacements In the case of Love waves there is just one degree of freedom perpendidular to plane ofpropagation while in case of Rayleigh waves there are two degrees of freedom in the plane of propagation It has been proven that equations of these two types of waves are independent from each other in the two dimensional case Then it is possible in this case to consider only a single wave type for analyzing the soilmodelbeside considering soil as a two dimensional region does not imply huge estimation in the process ofanalysis Mentioning that the proposed method dealing with irregular boundaries has already been appliedsuccessfully to the propagation of Love waves in this thesis the method is extended to the case of Rayleighwaves The presented method is called the compacted hyperelements method CHM and is verified byseveral examples showing very good accuracy with regard to other methods These examples are problemswhich solved by other numerical or explicit methods In each of these examples it could be seen that theCHM method is an accurate and efficient method to analyze the unbounded strata Varying the number ofthe hyperelements and the thickness of the thin layers it is shown that the suggested method has a superiorefficiency over the existing methods for dynamic analysis of infinite media Keywords Green s functions Rayleigh wave propagation Thin layer method irregularboundaries the Compacted Hyperelements method CHM

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ارائه روش هايپر المانهاي فشرده براي محاسبه توابع گرين در محيط هاي نامنظم هندسي

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