[ Problem Description ]
[ I-Beam Cantilever ]
[ Finite Element Analyses ]
[ Input and Output Files ]
The purposes of this example are:
Displacements are computed for a cantilever beam having an I-shape cross section, and subject to two concentrated loads P = 1600 lb at the flanges of the free end in opposite direction along y axis.
Details of the I-beam geometry and externally applied loads are shown in Figure 1.
The cantilever beam has length L = 40 inches, height h = 5 inches, width w = 10 inches, and thickness t = 0.25 inches. It is constructed entirely from one material type -- Young's Modulus E = 10^7 psi and Poisson's Rate = 0.3.
Finite element analyses are computed for a variety of mesh geometrys, and compared against the results for ANSYS-5.0 shell element, and the SAP-90 shell element.
Each segment of the I-beam is modeled with five shell finite elements, four for the flanges, and 1 shell element for the I-beam web. The overall mesh geometry is controled by the parameter N in Figure 1. N = 2 means that the I-beam is modeled with only two sets of shell finite elements along its length (i.e. 10 finite elements in total).
The ANSYS-5.0 shell element is a four node flat shell element having six degrees of freedom per node in which a drilling degree of freedom based on an approach suggested by Kanok-Nukulchai . The SAP-90 shell element is a quadrilateral flat shell element (six degrees of freedom per node).
|ALADDIN's Shell Element (x 0.1)||2.45142||2.50528||2.51482||2.52135|
|ANSYS-5.0 Shell Element (x 0.1)||1.1280||1.8943||2.3378||2.5135|
|SAP-90 Shell Element (x 0.1)||2.0218||2.3010||2.4562||2.5195|
|ALADDIN's Shell Element (x 0.01)||1.38753||1.46572||1.48824||1.49583|
|ANSYS-5.0 Shell Element (x 0.01)||0.6299||1.1112||1.3743||1.4601|
|SAP-90 Shell Element (x 0.01)||1.0434||1.3116||1.4407||1.4833|
Tables 1 and 2 summarize the transverse and horizontal displacements at Point 1 (see Figure 1) for a variety of finite element meshes. For the purposes of numerical comparison, displacements are also shown for shell elements in the ANSYS-5.0 and SAP-90 finite element packages.