Morphing of Plane Element to Beam Element for Static, Buckling, and Free Vibration Analysis

Static and dynamic analysis of beams is widely used in engineering problems. In this paper, morphing of plane element to beam element will be used for static, buckling, and free vibration analysis. The formulation of the proposed plane element begins with the writing of Taylor's expansion of the strain field. Selecting a complete first-order polynomial for strain field will eliminate some common errors such as parasitic shear error and sensitivity to distortion and rotation of the coordinate axes. Furthermore, establishing equilibrium equations of the plane problem reveals dependencies between the strain states. These dependencies, in addition to reducing the number of unknowns, will improve the efficiency of proposed element. By calculating the conversion matrix, the proposed beam element is created based on the suggested plane element. This matrix helps to calculate the stiffness, mass, and geometric stiffness matrices of the proposed beam element. Several benchmark tests will use to demonstrate the efficiency of the new element. For comparison, results of other researchers' good plane and beam elements will be available. In these numerical tests, the good accuracy of the proposed element in static, buckling, and free vibration analysis of beams with different boundary conditions and different aspect ratios will be proved.