A new nine-node element for analysing plates with varying thickness using basic displacement functions

The capability of the Finite Element Method in producing accurate and efficient results largely depends on the shape functions adopted to frame the displacement field inside the element. In this paper, a new nine-node Lagrangian element was developed to analyse thin plates with varying cross-sections using the shape functions obtained for non-prismatic straight beams with minimum number of elements. The formulated shape functions, which represent vertical displacements and rotations throughout elements, are rooted from a purely mechanical functions called Basic Displacement Functions (BDFs). These functions are obtained by implementing the force method in Euler–Bernoulli beam theory, which ensures that equilibrium equation is satisfied in all interior points of elements. To verify the competency of the proposed element, solutions for the static analysis of isotropic rectangular plates under various loading conditions, together with free vibration analysis of plates with linear thickness variation were obtained and compared with the previous literature. Results showed that the proposed nine-node Lagrangian element was computationally more cost-effective compared to other competing methods when small number of elements is employed.

Derivation of an Efficient Non-Prismatic Thin Curved Beam Element Using Basic Displacement Functions

The efficiency and accuracy of the elements proposed by the Finite Element Method (FEM) considerably depend on the interpolating functions, namely shape functions, used to formulate the displacement field within an element. In this paper, a new insight is proposed for derivation of elements from a mechanical point of view. Special functions namely Basic Displacement Functions (BDFs) are introduced which hold pure structural foundations. Following basic principles of structural mechanics, it is shown that exact shape functions for non-prismatic thin curved beams could be derived in terms of BDFs. Performing a limiting study, it is observed that the new curved beam element successfully becomes the straight Euler-Bernoulli beam element. Carrying out numerical examples, it is shown that the element provides exact static deformations. Finally efficiency of the method in free vibration analysis is verified through several examples. The results are in good agreement with those in the literature.

The Study for the Critical Moment of Arches in the Action of Endmoment Considering Shear Lag

Based on six basic assumptions and deformation behaviour, the total potential energy of arches are obtained. The basic displacement functions are expressed with spline function. According to minmum potential energy principle, the characteristic equation is deducted. The characteristic value is solved by multiplication power method. An exampleof arches in the action of endmoment is calculated. The critical positive and negtive moment of out-of-plane stability in arches with single sysmetry axis section are studied.