• Yiming Xu

Student thesis: Phd


The anisotropic laminate problem is difficult to solve exactly through the existing composite laminate theories. To fill this research gap, the present thesis performs a 3D analysis on anisotropic plates and laminates with various boundary conditions through the state space method (SSM). The idea of current research originates from some previous state space researches on orthotropic plates and laminates. However, because of the characteristic shear-extensional coupling and shear-shear coupling effects of anisotropic material, the previous state space researches which used the Navier-type solution (the sine-cosine Fourier series) for orthotropic cases are not applicable anymore. To overcome this difficulty, the author employs the in-plane complex Fourier series into derivation based on the state space equation which is derived from the fundamental linear-elastic equations of anisotropic material. This innovative idea simplifies the state matrix with differential operators into a determinate algebraic matrix and makes further state space analysis feasible. Conforming to different boundary problems of plates and laminates, different superposition solutions are suggested as the boundary conditions are rewritten correspondingly by using a differential treatment. The equations for boundary conditions are combined with the state space equation for anisotropic material, forming a new compound state space which represents the 3D anisotropic plate and laminate with all boundary conditions satisfied. Through employing SSM, a set of solvable linear equations are formed in the compound state space, and the exact solution for the problem desired is hence sought. Some numerical calculations for formulations of the present method are provided in this thesis, as case studies and application investigations. For illustration and comparison purposes, the accuracy and efficiency of various other theoretical analyses and the finite element method can hence be checked quantitatively with the present exact anisotropic 3D solutions.
Date of Award31 Dec 2022
Original languageEnglish
Awarding Institution
  • The University of Manchester
SupervisorQing Li (Supervisor) & Jack Wu (Supervisor)


  • anisotropic material
  • state space method
  • rectangular plates and laminates
  • boundary conditions

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