Eigen vector buckling based boundary analysis method for free vibration of rectangular thin plates
The main research topic of this paper is the application of the finite element method boundary analysis theory to study the stability of plate in irregular shape. First of all, the basic theory of free vibration of elastic plate and the basic equations of elastodynamics are introduced, and the governing equation of small deflection of free vibration of plate is given. Secondly, the finite element method boundary analysis method is introduced in details, including the basic idea and analysis steps of finite element method boundary analysis, and some element types, so as to lay a theoretical foundation for better understanding of finite element method boundary analysis method and application of it to analyze the stability of plate. At last, finite element method boundary analysis is applied to analyze the stability of plate, among which, the structural analysis types in ANSYS software and its analysis steps are introduced, and buckling (eigenvalues) analysis in ANSYS software is mainly introduced, and the effective performance of algorithm is verified by applying ANSYS software.
Weak form quadrature element method for accurate free vibration analysis of thin skew plates
In this paper, a novel weak form quadrature element method (QEM) is proposed for accurate free transverse vibration analysis of thin isotropic skew plates with general boundary conditions. In the formulation of the stiffness matrix, the first and second order derivatives of the shape functions at integration points are computed explicitly by using the differential quadrature rule. This leads to a great simplicity in formulating an N × N -node quadrature plate element and a large reduction of programming effort. Different from the existing weak form quadrature element method or differential quadrature finite element method, the element nodes can be either the same or different from the integration points. Convergence studies are performed. Free vibration of skew thin plates with various skew angles and different combinations of boundary conditions is analyzed. It is shown that although the assumed displacement field does not explicitly consider the bending moment singularities at the obtuse angles, the proposed QEM can yield accurate frequencies even for the thin isotropic skew plate with large skew angles.
Flow in a branching open channel: a review
Branching channel flow refers to any side water withdrawals from rivers or main channels. Branching channels have wide application in many practical projects, such as irrigation and drainage network systems, water and waste water treatment plants, and many water resources projects. In the last decades, extensive theoretical and experimental investigations of the branching open channels have been carried out to understand the characteristics of this branching flow, varying from case studies to theoretical and experimental investigations. The objectives of this paper are to review and summarise the relevant literatures regarding branching channel flow. These literatures were reviewed based on flow characteristics, physical characteristics, and modeling of the branching flow. Investigations of the flow into branching channel show that the branching discharge depends on many interlinked parameters. It increases with the decreasing of the main channel flow velocity and Froude number at the upstream of the branch channel junction. Also it increases with the increasing of the branch channel bed slope. In subcritical flow, water depth in the branch channel is always lower than the main channel water depth. The flow diversion to the branch channel leads to an increase of water depth at the downstream of the main channel. From the review, it is important to highlight that most of the study concentrated on flow characteristics in a right angle branch channel with a rigid boundary. Investigations on different branching angles with movable bed have still to be explored.