Afamilyofunconditionallystabledirectintegrationalgorithmwithcontrollablenumericaldissipationsisproposed.Thenumericalpropertiesofthenewalgorithmsarecontrolledbythreeparametersα,βandγ.Bytheconsistentandstabilityanalysis,theproposedalgorithmsachievethesecond-orderaccuracyandareunconditionallystableundertheconditionthatα≥-0.5,β≤0.5andγ≥-(1+α)/2.Comparedwithotherunconditionallystablealgorithms,suchasChang’salgorithmsandCRalgorithm,theproposedalgorithmsarefoundtobesuperiorintermsofthecontrollablenumericaldampingratios.Theunconditionalstabilityandnumericaldampingratiosoftheproposedalgorithmsareexaminedbythreenumericalexamples.Theresultsdemonstratethattheproposedalgorithmshaveasuperiorperformanceandcanbeusedexpedientlyinsolvinglinearelasticdynamicsproblems.
