Scaled boundary finite element method for 2D and 3D acoustic-structure interaction analyses considering structural elastoplasticity

Abstract

The acoustic-structure interaction commonly exists in numerous civil and mechanical engineering applications, such as dam-reservoir interaction system, air-coupled ultrasonic testing and the design of underwater structures. In all these applications, the acoustic domains are usually infinitely large. Moreover, the distinct physical properties of acoustic and structural domains lead to the preference of using different mesh sizes for each domain in numerical modelling. Due to the intrinsic nature of scaled boundary finite element method in modelling unbounded domain and its versatility in mesh generation. This thesis presents the developments of this method for simulating 2D and 3D acoustic-structure interaction systems by considering the infinite acoustic domain and structural elastoplasticity, which frequently appears under strong excitations. The high-order doubly-asymptotic open boundary is developed to simulate the wave propagation in 2D and 3D exterior acoustics accurately and efficiently. This is accomplished by solving the scale boundary finite element equation for unbounded acoustic domain in the frequency domain using doubly-asymptotic continued fractions. Via introducing the auxiliary variables, this open boundary can be formulated into a system of time-domain equations and thus suitable for non-linear analysis. For the elastoplastic analysis of structures, the efficient scaled boundary formulation for elastoplasticity with stabilization is extended to 3D analysis. In this formulation, the computationally expensive return-mapping algorithm is only required to be performed at scaling centres as the elastoplastic constitutive matrices and internal stresses are assumed to be constants within each subdomain. Stabilisation matrices are introduces to control spurious modes. Additionally, Newmark's scheme is employed for dynamic elastoplastic analysis. Mesh generation from the STL models of the whole system and mesh transition on the acoustic-structure interface, especially for 3D models with complex geometry, can be easily addressed with automatic mesh generation techniques, which benefit from the boundary discretization in scaled boundary finite element method. Both 2D and 3D numerical examples are presented in this thesis to highlight the accuracy, efficiency and robustness of the proposed techniques for the numerical simulations of acoustics, elastoplastic structures and acoustic-structure interaction problems.