Imperfection sensitivity analysis of laminated folded plates

Advantages of the mixed format in geometrically nonlinear analysis of beams and shells using solid finite elements

“…The asymptotic approach, derived as a FE implementation [25,28,29,32,34,[36][37][38][39][40][41][42][43][44] of the Koiter theory of elastic stability [45] provides an effective and reliable strategy for predicting the initial post-critical behavior in both cases of limit or bifurcation points and makes the imperfection sensitivity analysis easy and affordable [26,27,33,35,[46][47][48]. The solution process is based on a third-order Taylor expansion of Equation (1), in terms of load factor and modal amplitudes i .…”

Koiter Asymptotic Analysis of Thin-walled Cold-formed Steel Uprights Pallet Racks

“…The finite element analysis was carried out following [9,10] and using the finite element described in [18][19][20]. The boundary conditions for simulation of the rack were considered as pinned at one end and simply supported at the other one (see Fig.…”

“…The use of corotational formulation, within a mixed formulation, allows to have a general finite element implementation of Koiter's analysis [7,8]. Our recent technology [9][10][11], in terms of numerical implementation, is applied to the evaluation of the performance of slender cold-formed steel members especially for the case of modal interaction. In particular, an efficient and robust imperfection sensitivity analysis is performed.…”

Mixed Solid Models in Numerical Analysis of Slender Structures

“…2.3 Advantages of mixed solid finite elements in path-following and asymptotic analysis of slender structures FE models directly derived from the 3D continuum using the Green strain measure have a low order dependence on the strain energy from the discrete FE parameters: 3rd and 4th order for mixed and compatible respectively. On the contrary geometrically exact shell and beam models [5,6] or those based on corotational approaches [26,47,51], explicitly make use of the rotation tensor and its highly nonlinear representation. This implies that the strain energy is infinitely differentiable with respect to its parameters and leads to very complex expressions for the energy variations with a high computational burden of path following and much more of asymptotic analyses.…”