A proposed standard set of problems to test finite element accuracy

A physically stabilized and locking-free formulation of the (SHB8PS) solid-shell element

“…This test problem has become very popular and it has been used by many authors since (MacNeal et al, 1985). It is very severe since the transverse shear and membrane locking phenomena are very important and emphasized by the problem geometry (distorted, skewed elements).…”

“…Except for the symmetry, the boundary conditions are free; nevertheless, the displacement of one point in the z-direction is fixed in order to prevent rigid body motions. According to the reference solution (MacNeal et al, 1985), the displacement of point A along the x-direction equals 0.0924 (see Figure 7). The convergence results are reported in Table 4 in terms of the normalized displacement at point A in the x-direction.…”

“…This second, out-of-plane loading case consists of a horizontal unit load P=1 in the y-direction (see Figure 8). The reference solution is also given by (MacNeal et al, 1985). For this P2 loading, the displacement at point A in the loading direction (see Figure 8) should be equal to 1.754×10 -3 .…”

“…In this first case, the unit load is applied in the plane of the beam along the vertical z-direction (see Figure 8). The analytical tip displacements in the loading directions are given in (MacNeal et al, 1985). For the loading case P1, the displacement at point A in the loading direction Oz (see Figure 8) should be equal to 5.424×10 -3 .…”

“…This test has been introduced by (MacNeal et al, 1985) and has been extensively used to test the elements performance due to the use of warped configuration. It is considered now as a reference shell test (see Batoz et al, 1992).…”