حل ديناميكي ورق ايزوتروپ و كامپوزيت در حوزه فركانس با استفاده از توابع پايه نمايي

چكيده انگليسي :

Transient Analysis of Isotropic and Composite Laminated Plates in Frequency Domain Using Exponential Basis Functions Atefeh Pirzadeh atefeh pirzadeh@gmail com Date of Submission January 23 2014 Department of Civil Engineering Isfahan University of Technology Isfahan 84156 83111 IranDegree M Sc Language FarsiSupervisor Dr Bijan Boroomand boromand@cc iut ac ir Advisor Dr Mojtaba Azhari mojtaba@cc iut ac ir Abstract In this dissertation transient analysis of thin and moderately thick isotropic and laminated compositeplates is studied through analyzing the problems in frequency domain and using a mesh free method To thisend plate theories such as the classical plate theory CLPT the first order shear deformation theory FSDT the third order shear deformation theory TSDT and the higher order Zig Zag theory proposed byCho and Parmerter have been used Moreover wave propogation in thin isotropic plates is studied using thefirst order shear deformation theory in frequency domain Since in this study the problems are defined without the effects of viscous damping the exponentialwindow method EWM is used to introduce adequate damping to perform inverse Fourier transformation Inthis method an artificial damping is added to the governing equations and after evaluation of the solution itseffect is removed The solution method used in this research is of a Trefftz type and may be classified in the category ofmesh free methods In this mesh free method the solution is split into homogeneous and particular parts Exponential basis functions EBFs are then used for both parts of the solution For the homogeneoussolution a series of exponential basis functions satisfying the homogeneous part of the governong equations are considered The coefficients of these EBFs are determined by satisfying boundary conditions on somediscrete boundary points The coefficients are obtained through a discrete transformation technique It hasbeen shown that the particular response can be approximated by two approaches i e using a separate seriesof EBFs or employing Fourier series In this study the first approach is used for smooth loads and the secondone is utilized for the singular loads In the first approach the particular solution is expressed as a series ofexponential basis functions not satisfyling the homogeneous part of the governing equations The externalload function is approximated by the same EBFs with the use of some discrete domain points Loadcoefficients are calculated by means of a similar transformation as used in the homogenous solution Bysatisfying the non homogeneous governing equations the coefficients of the basis functions are evaluated To demonstrate the accuracy and the efficiency of the method used in this thesis the solution of variousproblems such as isotropic and laminated composite plates with different shapes and boundary conditions ispresented The numerical results of these analyses are compared with those of the exact solutions if available for each theory used The results are also compared with those obtained from 3D finite element method modeled in ANSYS In wave propogation problems the group velocity of waves is compared with the exactone obtained from FSDT formulation It has been concluded that the proposed method is capable ofproducing results with excellent accuracy in transient analysis of plates through analyzing them in frequencydomain Key words Isotropic plates Laminated composite plates Exponential basis functions Frequency domain

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حل ديناميكي ورق ايزوتروپ و كامپوزيت در حوزه فركانس با استفاده از توابع پايه نمايي

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