Infinite Element Static‐Dynamic Unified Artificial Boundary

Abstract

The method, which obtains a static-dynamic comprehensive effect from superposing static and dynamic effects, is inapplicable to large deformation and nonlinear elastic problems under strong earthquake action. The static and dynamic effects must be analyzed in a unified way. These effects involve a static-dynamic boundary transformation problem or a static-dynamic boundary unified problem. The static-dynamic boundary conversion method is tedious. If the node restraint reaction force caused by a static boundary condition is not applied, then the model is not balanced at zero moment, and the calculation result is distorted. The static numerical solution error is large when the structure possesses tangential static force in a viscoelastic static-dynamic unified boundary. This paper proposed a new static-dynamic unified artificial boundary based on an infinite element in ABAQUS to solve static-dynamic synthesis effects conveniently and accurately. The static and dynamic mapping theories of infinite elements were introduced. The characteristic of the infinite element, which has zero displacement at faraway infinity, was discussed in theory. The equivalent nodal force calculation formula of infinite element unified boundary was deduced from an external wave input. A calculation and application program of equivalent nodal forces was developed using the Python language to complete external wave inputting. This new method does not require a static and dynamic boundary transformation and import of stress field and constraint counterforce of boundary nodes. The static calculation precision of the infinite element unified boundary is more improved than the viscoelastic static-dynamic unified boundary, especially when the static load is in the tangential direction. In addition, the foundation simulation range of finite field can be significantly reduced given the utilization of the infinite element static dynamic unified boundary. The preciseness of static calculation and dynamic calculation and static-dynamic comprehensive analysis are unaffected.

Nonlinear Behaviour of Concrete Buttress Dams under High‐Frequency Excitations Taking into Account Topographical Amplifications

“…e behaviour of buttress dams, both in the stream and cross-stream directions, is investigated using three-dimensional finite element modelling. Topographic amplifications are considered using the direct finite element method (FE) (Lokke and Chopra [16]) and the analytical approach (Song et al [20]). e results are also compared with those of the massless method.…”

Modification Research of the Internal Substructure Method for Seismic Wave Input in Deep Underground Structure‐Soil Systems

“…e representative achievements in the artificial boundaries include the boundary element method [9,10], the infinite element method [11], perfectly matched layers [12,13], transmitting boundaries [14,15], viscous boundaries [16], viscoelastic boundaries [17,18], and exact absorbing boundaries [19,20]. However, due to the application of the artificial boundaries, a new problem appears in inputting the seismic waves into the finite model without affecting the transmission of outgoing waves.…”