Corotational nonlinear dynamic analysis of laminated composite shells

Continuous inter-laminar stresses for regular and inverse geometrically non linear dynamic and static analyses of laminated plates and shells

“…Although the Newmak´s time integration has been proved to work properly for geometrical non-linear dynamics described by Total Lagrangian formulations [14,15,16,17]; this example has been recently presented by [8] with the citation "It has been shown in previous works [61,62] that the classical Newmark method fails when applied for the time integration in this problem". We know, but not all readers know, that the referred authors were thinking only about Updated Lagrangian formulations; therefore, this example is presented here to clarify this subject for readers not used to total Lagrangian formulations.…”

“…Following [8], the dynamic analysis of the isotropic cantilever beam of Figure 14 under a uniformly distributed vertical load is performed. .…”

“…One should not forget that, in updated Lagrangian formulations velocity and acceleration should be transformed from spatial to material reference frame by formulas associated with the finite rotation. This process should be satisfactorily treated using specially developed time integrators, see references [8,9,10,11,12,13]. As total Lagrangian formulations for the dynamic analysis of structures are practically inexistent, most authors of updated Lagrangian formulations, mainly co-rotational, indicate that the Newmark algorithm cannot be used for non-linear dynamic analysis.…”

Dynamic Response Of Laminated Composite Shells Subjected To Impulsive Loads

“…Also, the concurrent effect of material degradation due to impact damage was investigated. F. S. d. Almeida and A. M. Awruch, [5] presented a numerical study on the dynamic analyses of laminated composite shells considering geometrically nonlinear effects. To perform the dynamic analysis, the algorithm employed for the analysis was composed by a linear composite shell element which it was associated with the element independent corotational formulation to account the geometric nonlinearity.…”

A time-domain finite element method for seakeeping and wave resistance problems

“…An energy conserving/decaying time-stepping algorithm has been used for the dynamic analysis of the problem [72,73,74]. This approach ensures the stability in the non-linear geometric range.…”