Dynamic Analysis of Thick Plates Including Deep Beams on Elastic Foundations Using Modified Vlasov Model

Abstract

Dynamic analysis of foundation plate-beam systems with transverse shear deformation is presented using modified Vlasov foundation model. Finite element formulation of the problem is derived by using an 8-node (PBQ8) finite element based on Mindlin plate theory for the plate and a 2-node Hughes element based on Timoshenko beam theory for the beam. Selective reduced integration technique is used to avoid shear locking problem for the evaluation of the stiffness matrices for both the elements. The effect of beam thickness, the aspect ratio of the plate and subsoil depth on the response of plate-beam-soil system is analyzed. Numerical examples show that the displacement, bending moments and shear forces are changed significantly by adding the beams.

Critical velocity of a uniformly moving load on a beam supported by a finite depth foundation

“…In dynamic analyses, foundation mass is usually added inconsistently according to linear shape function to the structure mass [26]. Then often, the finite element approach is employed.…”

“…Results of such analyses are dependent on the value of the soil depth, H, which can either be the actual depth at which a stiff substratum is located or a depth after which no appreciable soil deformation occurs. In [24][25][26] the surface at depth H is simply designated as a rigid base and as such, must be determined from the geological conditions. Dynamic interaction between a beam and a foundation of finite depth is presented in [27], but solely vertical soil vibrations are considered.…”

“…But in other works, e.g. [27], the surface located at depth H is simply designated as a rigid base, similarly as in the developments related to the Vlasov model [24][25][26]. With the finite depth introduced, it is possible to account for beam and foundation interaction which ensures a smooth transition of the critical velocity between the two known values, namely the one given by the classical formula (1) and the one related to the lowest wave velocity of propagation in the foundation.…”

“…Simplifications introduced in this paper are: (i) the foundation model is presented under plane strain condition and (ii) horizontal soil displacements are neglected (as in [24][25][26][27][28]). A new formula for the critical velocity is derived and it is shown, that the critical value depends on the mass ratio defined as the square root of the fraction of the foundation mass to the beam mass.…”

Impact of nonlinearity on bolt forces in multi-bolted joints: A case of the assembly stage

“…The Winkler elastic foundation model [31] is added between the joined elements as a model of the contact layer. This type of a contact layer model can be characterized by l one- 5 where K is the stiffness matrix of the multi-bolted system, q is the displacements vector of the multi-bolted system, and p denotes the loads vector of the multi-bolted system.…”