Bending strength predictions of cross-laminated timber plates subjected to concentrated loading using 3D finite-element-based limit analysis approaches

An algorithm for adaptive introduction and arrangement of velocity discontinuities within 3D finite-element-based upper bound limit analysis approaches

“…Since neither an exact solution nor a reference value is available for this example, the obtained upper bounds are compared to a solution without velocity discontinuities but with a very fine mesh consisting of 55571 tetrahedral elements, shown in Figure 16a. Additionally, the 3D lower bound formulations proposed by the authors in [50] was applied to enclose the exact collapse load multiplier β * , giving The total CUP time for the upper bound as well as lower bound calculation with the fine mesh were 10.6 min and 18.6 min, respectively. The upper bound obtained with velocity discontinuities, β = 2.0785, can thus be considered as reliable, since it is located within the bound gap given in Eq.…”

“…Recently, an alternative approach has been presented by the authors [44], where finite-element-based upper bound formulations with sensibly-arranged velocity discontinuities have been proven reliable and efficient, without the need of intensive mesh refinement in failure regions. Additionally, although the implementation of orthotropic yield functions in numerical upper bound formulations has been presented in several publications [45,46,47,48,49,50], to the authors' knowledge, the combination of orthotropic yield functions and velocity discontinuities was presented by the authors in [44] for the first time. In order to apply this approach to more general problems, in this paper, a comprehensive introduction on the numerical implementations as well as an adaptive introduction and adjustment strategy on the sensible arrangement of velocity discontinuities will be presented.…”