Overview

Test Case

A beam of length and width w, made up of two layers of different materials, is subjected to a uniform rise in temperature from T_ref to T_o and a bending moment M_y at the free-end. Determine the free-end displacement δ (in the Z-direction) and the X- direction stresses at the top and bottom surfaces of the layered beam. E_i and α _i correspond to the Young's modulus and thermal coefficient of expansion for layer i, respectively.

Figure 200: Composite Beam Problem Sketch

Analysis Assumptions and Modeling Notes

The beam is idealized to match the theoretical assumptions by taking ν = α _y = α _z = 0. Nodal coupling of the ROTY degree of freedom is used for the SHELL281 model to apply the uniform edge moment. Opposing nodal forces are applied at the top and bottom edges of the free end for the SOLSH190 model to apply the end moment. The magnitude of these applied nodal forces is calculated as: FX = M_y/(2 * (t₁+t₂)) = 10/0.6 = (100/6). POST1 is used to obtain the nodal stresses and displacements.

For the fourth model (SHELL281), two sets of four overlapping elements (a total of eight SHELL281 elements) are used. Each set represents a single layer. The set of four elements representing the lower layer has its nodal plane located on the "top" face whereas the set of elements corresponding to the top layer has its nodal plane located on the "bottom" face. The combination of overlapping elements thus defines a two-layered beam with its nodal plane at the interface between the layers (offset from the middle plane).

The second model uses eight SOLID186 elements (each with 2 layers), similar to the fourth SHELL281 model. Tapered pressure is applied on the end face to apply moment.

The third model uses eight SOLSH190 elements (each with 2 layers).

Results Comparison