Isogeometric Analysis Of Free Vibration And Exact Solutions Of Random Vibration For Thin Shell Structures

Shells are thin-wall structure with light weight and high efficiency,appear in various forms in nature and engineering products.Thin shells are widely used in aerospace,marine and automotive,civil and mechanical engineering because of its high ratio of load-carrying capacity to self-weight.As a result of wide usage in engineering,it is common for shell structures to be exposed to external excitations induced by wind pressure,jet noise,turbulent boundary layer,ocean waves and earthquake,which is random in nature.Furthermore,the mechanical behavior of shell structures is complicated because of its various geometry and external excitation,so it is of great significance to predict its dynamic responses effectively and accurately.To extend applications of the emerging isogeometric analysis and to obtain benchmark solutions of random vibrations for shell structures,isogeometric analysis of free vibration and exact solutions of random vibration for thin shell structures are studied in this thesis.The main contents are as follows:Firstly,the free vibrations of thin shell structures are studied by isogeometric analysis,which has potential to integrate CAD and CAE.Isogeometric thin shell element based on Kirchhoff-Love theory,combined with advanced isogeometric analysis technologies for thin shell comprised of multiple patches and trimmed shell structures,is used in isogeometric free vibration analysis of thin shells.Shell structures are modeled through modeling software Rhinoceros,then geometry information of NURBS surface,which is extracted from the IGES file,is used directly for analysis.Without the need to mesh,seamless connection between CAE and CAD is achieved.Through comparisons of results of free vibration of thin shell structures by isogeometric analysis and other numerical methods,it can be concluded that higher effectiveness and accuracy can be achieved by isogeometric analysis compared to other numerical methods.Then,the framework for exact analytical solution of stationary random vibration of thin shell structures is presented,exact random responses with good efficiency are achieved.Random vibration analysis for thin shell structures are transformed to deterministic vibration analysis by incorporating Pseudo Excitation Method and exact frequencies and mode shapes for thin shell structures.Taking closed and open cylindrical shells as examples of analysis,Power Spectral Density(PSD)and Root Mean Square(RMS)of random responses of closed and open cylindrical shells simply supported at all edges under varied excitation are computed.PSD curves and RMS of membrane force and bending force are evaluated as well.To validate the framework proposed,same problems are performed by commercial FEM program ABAQUS,and comparison is made.It is indicated that the proposed method is more accurate than FEM.It should be noted that when it comes to random vibration analysis of thin shell structure under external excitation with high frequencies,the advantages of the proposed method become more evident compared to finite element method.The exact solutions can be used as benchmarks for researchers to check their numerical results and for engineering design.