PSI - Issue 78

Stefano Ercolessi et al. / Procedia Structural Integrity 78 (2026) 1497–1504

1501

3. Numerical application of the proposed workflow

In the following section, a numerical application of the proposed open-source FEA workflow is presented. The case study consists of a typical two-dimensional SSI model, which is a well-established benchmark in earthquake and civil engineering. This type of model is particularly suitable for illustrating the capabilities of the proposed methodology, as it involves multiple interacting components that must be accurately modelled using the functions described in the previous sections. The system comprises a moment-resisting steel frame founded on a shallow foundation, resting on a deformable soil domain. The entire assembly is subjected to a weak seismic input motion. This configuration allows the demonstration of various modelling aspects, such as the definition of structural and geotechnical elements, boundary conditions, and dynamic loading, all within the integrated framework. The steel frame is characterized by four storeys and two bays. Columns and beams are modelled considering elastic beam-column elements available in OpenSees. The mechanical characteristics associated with these elements are reported in Tab. 1-2. The nodes in correspondence of the same floor are constrained relying on rigid diaphragm multi-point constrain where the central node is considered as primary node. Lumped masses are applied to the primary nodes. Specifically, the first three storeys are each assigned with a mass of 35.67 t, while the top storey carries a reduced mass of 26.76 t.

Table 1. Mechanical characteristics of columns. Description

Parameter

Unit

Elastic modulus Section area Section inertia

E col A col

210.00

GPa

2 4

112.00e-04

m m

I col

10160.00e-08

Table 2. Mechanical characteristics of beams. Description

Parameter

Unit

Elastic modulus Section area Section inertia

E col A col

210.00

GPa

2 4

83.40e-04

m m

I col

23457.00e-08

Moreover, equivalent static loads derived from the mass values are applied in the vertical direction for the gravity analysis and kept constant during the transient one. The foundation is designed with a base width of 12.00 m and a height of 3.50 m. It is discretized considering a structured mesh. SSPquad elements, available in the OpenSees framework, are associated with the Gmsh discretization. Elastic isotropic material is assigned to the foundation. The mechanical properties assigned to the foundation are summarized in Tab. 3.

Table 3. Foundation elastic isotropic mechanical parameters. Description Parameter

Unit

Elastic modulus Poisson’s ratio

E fnd ν fnd ρ fnd

210.00

GPa

0.45 2.50

−

3

t / m

Mass density

The connection between the foundation and the steel frame is explicitly modelled to ensure mechanical continuity. After, duplicating the nodes along the top edges of the foundation mesh, they are constrained to the original foundation edge using an equalDof constraints. The base nodes of the column elements are then connected to the duplicated nodes considering rigidLink constraints of beam type, each referring to the tributary area associated with the respective column. Soil-foundation interface also is modelled. The bottom nodes of the foundation are tied to the soil contact nodes using an equalDof constraint in both horizontal and vertical directions. For the lateral edge of foundation, only the horizontal degree of freedom is tied with the correspondent soil nodes. The soil and foundation mesh generated