Development of High-Order Infinite Element Method for Bending Analysis of Mindlin–Reissner Plates

An approach is presented for solving plate bending problems using a high-order infinite element method (IEM) based on Mindlin–Reissner plate theory. In the proposed approach, the computational domain is partitioned into multiple layers of geometrically similar virtual elements which use only the data of the boundary nodes. Based on the similarity, a reduction process is developed to eliminate virtual elements and overcome the problem that the conventional reduction process cannot be directly applied. Several examples of plate bending problems with complicated geometries are reported to illustrate the applicability of the proposed approach and the results are compared with those obtained using ABAQUS software. Finally, the bending behavior of a rectangular plate with a central crack is analyzed to demonstrate that the stress intensity factor (SIF) obtained using the high-order PIEM converges faster and closer than low-order PIEM to the analytical solution.

Spectral Stochastic Infinite Element Method in Vibroacoustics

A novel method to solve exterior Helmholtz problems in the case of multipole excitation and random input data is developed. The infinite element method is applied to compute the sound pressure field in the exterior fluid domain. The consideration of random input data leads to a stochastic infinite element formulation. The generalized polynomial chaos expansion of the random data results in the spectral stochastic infinite element method. As a solution technique, the non-intrusive collocation method is chosen. The performance of the spectral stochastic infinite element method is demonstrated for a time-harmonic problem and an eigenfrequency study.

A Benchmark Study on Eigenfrequencies of Fluid-Loaded Structures

In this paper, a coupled finite/infinite element method is applied for computing eigenfrequencies of structures in exterior acoustic domains. The underlying quadratic eigenvalue problem is addressed by a contour integral method based on resolvent moments. The numerical framework is applied to an academic example of a hollow sphere submerged in water. Comparisons of the computed eigenfrequencies to those obtained by boundary element discretizations as well as finite element discretizations in conjunction with perfectly matched layers verify the proposed numerical framework. Furthermore, extensive parameter studies are carried out illustrating the performance of the method with regard to both projection and discretization parameters. Finally, we point out that the proposed method achieves significantly smaller residuals of the computed eigenpairs than the Rayleigh Ritz procedure with second-order Krylov subspaces.

An Element-Free Galerkin Coupled with Improved Infinite Element Method for Exterior Acoustic Problem

It is known that the variable-order infinite acoustic wave envelope element (WEE) must be coupled with finite element method (FEM) by element matching for computing acoustic field radiated from radiators with complex geometric shapes. Therefore, the WEEs have to be reconstructed when the finite elements are refined or changed. To overcome the shortcoming, the element-free Galerkin (EFG) coupled with improved WEE (IWEE) method is presented to compute acoustic problems in the infinite domain. The continuity and compatibility of the acoustic pressure are maintained by IWEE that is composed of a standard WEE and a fictitious finite mesh. A key feature of the method is the introduction of the EFG method which is employed to eliminate the element matching and improve the accuracy of predicted acoustic pressure. The factors that affect the performance of the method are investigated by numerical examples, which include shape function construction, the weight function and the size of the influence domain. The numerical results show that the present method provides more accurate results compared to the coupled FEM-WEE method. The experimental results show that the method is very flexible for acoustic radiation prediction in the infinite domain.

Experimental Research on the Effect of Wing Structure on Aeroelasticity Phenomenon

Aeroelasticity on airplane wing has a significant impact on the efficiency and the safety of a flight. Therefore, the study of aeroelasticity problems is a great attention in wing design process. To analyze this, three primary subjects of aeroelastic phenomena that the examination has to focus on, which are wingtip oscillation amplitude, flutter frequency and critical flutter velocity of the wing. [1] As these subjects are highly dependent on structures and materials of the wings, therefore, the aim of this paper is to introduce a structural calculation which is the combination of three experimental models and the infinite element method. Supercritical is chosen as the sample airfoils of the simulation. The model wings are made from different materials and size in order to create varied wing structures, thereby a comprehensive analysis is accomplished and the flutter velocity is also restricted to appropriate values within the working range of experiment devices. Simultaneously, Infinite element method using ANSYS software to simulate the phenomena on the same model wings is also conducted as a verification for the precision of the experimental models. In conclusion, obtained results from the structural calculation have a high applicability in the preliminary design stage of airplane wings, by making comparisons between two or more chosen airfoils to conclude which is the better one in term of wing sustainability and aeroelasticity resistance.