Abstract
The curved beam with a great initial curvature is the typical structure and applied widely in real engineering structures. The common practice in the current literature employs two‐node straight beam elements as the elementary members for stress and displacement analysis, which needs a large number of divisions to fit the curved beam shape well and increases computational time greatly. In this paper, we develop an improved accurate two‐node curved beam element (IC2) in 3D problems, combining the curved Timoshenko beam theory and the curvature information calculated from the same beam curve. The strategy of calculating the curvature information from the same bean curve in the IC2 beam element and then transferring the curvature information to the two‐node straight beam element can greatly enhance the accuracy of the mechanical analysis with no extra calculation burden. We then introduce the finite element implementation of the IC2 beam element and verify by the complex curved beam analysis. By comparison with simulation results from the straight two‐node beam element in the MIDAS (S2‐MIDAS) and the three‐node curved beam element adopted in the ANSYS (C3‐ANSYS), the simulation results of the typical quarter arc examples under constant or variable curvature show that the IC2 beam element based on curved beam theory is a combination of efficiency and accuracy. And, it is a good choice for analysis of complex engineering rod structure with large initial curvature.
Highlights
Three-Dimensional Curved Beam Theory and Its Finite Element FormulationWe firstly summarize the basic three-dimensional curved beam theory which has been presented by Reissner [27]
Over these considerations, the two-node general curved beam element is the best choice of a combination of Advances in Materials Science and Engineering y R
We introduced the complete summary of the curved beam theory and its basic equations, which are considered in this paper
Summary
We firstly summarize the basic three-dimensional curved beam theory which has been presented by Reissner [27]. The finite element formulation of Reissner’s curved beam theory and its variational equations are introduced. Following Reissner’s curved beam theory, the strain measures, which are conjugated to the stress resultants and couples, are given as zu′ ε′ −. We introduced the complete summary of the curved beam theory and its basic equations, which are considered in this paper. Curvature information, which has been used in the curved beam theory, can enhance the accuracy of the numerical results compared with the straight beam element based on the straight beam theory. The accuracy of the curvature information, which is calculated and passed to the IC2 beam element, is extremely important for precisions of the numerical results of rods. (12d) and scheme B: we precalculate and save the curvature of the whole beam before we start to the numerical analysis of the complex rod structure and pass the curvature information to the IC2 beam element to start the mechanical analysis of the beam structure by the FE numerical calculations
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