ABSTRACT
Generalized Newmark method used to discrete time domain, i.e., the following integral format will be used:
u t un n n n= +u tu 2Δ Δ + 1 Δβ (4)
u tu t t un nu n nu n= + + 2
2 20Δ Δ+ 5 Δ Δ β (5)
The finite element balance equation of loading increment at No. n+1 steps obtained from Equation (3) is:
Put equation (4) and equation (5) into equation (6), the equation about Δun can be obtained:
K u Fn nΔ Δ (7)
where K represents equivalent stiffness matrix, K t t Fn+( . ) ( ) ;K0 1 1t M 2
2αβ ββ βΔΔ Δ Δ is is equivalent loading increment, ΔF Fn n −+1 ( ) , K u u tn n
n nu= ++α β) (M Δ 0 5 2. Δt un , u u tun
p n n= + Δ . As setting of parameter
β1, β2 values will affect the accuracy and stability of algorithm, in general, if β1 1 2= / and β2 1 1 4= / ~8 / are set, stabile solutions will be obtained. To solve linear equation group (7), the value of Δun can be obtained, by gradual iteration to achieve displacement of nodes, the state of unit stress can be obtained by using constitutive relationship so as to analyze the stability of the slope.
