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Basic concepts of numerical methods
Published in M.S. Cheung, W. Li, S.E. Chidiac, Finite Strip Analysis of Bridges, 1996
M.S. Cheung, W. Li, S.E. Chidiac
The discussion has so far been limited to the displacement-based finite element method since this is the most widely applied and recognized method of solution. The finite strip method can be regarded as a degenerate form of the finite element method which is used to primarily model the response of prism-like structures such as plates and solids. For example in plate bending problems, the finite element method requires that the element be capable of simultaneously modeling the deformation pattern in both directions, whereas the finite strip method models the problem as a one-dimensional strip in the longitudinal direction using an interpolation function for the displacement field that satisfies a priori the boundary conditions at both ends. The finite element requirements on the admissibility of the interpolation function also apply to the finite strip method with the exception of the rigid body modes. The exception arises from the finite strip requirements to satisfy the support boundary conditions a priori.
A new finite strip formulation based on Carrera unified formulation for the free vibration analysis of composite laminates
Published in Mechanics of Advanced Materials and Structures, 2022
Behnam Daraei, Saeed Shojaee, Saleh Hamzehei-Javaran
The finite strip method (FSM) has proved to be an efficient and inexpensive computational tool to analyze a wide range of structures with regular geometries such as rectangular plates and prismatic plates and shells, where a full finite element analysis is often extravagant and even unnecessary [34]. A main advantage of the FSM is that the orthogonality properties of the harmonic functions used along the nodal lines lead to decrease the computational cost and time. However, this method can only be used to analyze plates that have a regular geometry. The FSM allows rectangular plates to be discretized in one direction by finite strips which are connected to one another along the so-called nodal lines. The FSM can be considered as a simplified extension of the FE procedure. Unlike the standard FEM, which uses polynomial shape functions in both longitudinal and transverse directions, the FSM calls for use of simple polynomial shape functions in the one direction and continuously harmonic function series in the other one. These harmonic function series should satisfy the boundary conditions at two opposite edges of the plate (at the ends of the strips). However, the boundary conditions in two other edges of the plate can be arbitrary. More details and implementation of FSM have been comprehensively discussed in books by Cheung [34] and Cheung and Tham [35]. Moreover, the FSM was later widely used in various problems by many authors, for example, see Ref [36–40].