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A novel numerical formulation for solving fluid-structure interaction (FSI) problems is proposed where the fluid field is spatially discretized using smoothed particle hydrodynamics (SPH) and the structural field using the finite element…
In two and three dimensions, this study is focused on the numerical analysis of an eigenproblem associated with a fluid-structure model for sloshing and elasto-acoustic vibration. We use a displacement-Herrmann pressure formulation for the…
We develop a finite element discretization for the weakly symmetric equations of linear elasticity on tetrahedral meshes. The finite element combines, for $r \geq 0$, discontinuous polynomials of $r$ for the displacement,…
The multimesh finite element method enables the solution of partial differential equations on a computational mesh composed by multiple arbitrarily overlapping meshes. The discretization is based on a continuous--discontinuous function…
A robust $hp$-adaptive finite element framework is presented for the investigation of static cracks in materials characterized by complex, pointwise density variations. Within such heterogeneous media, the equilibrium equation governed by…
One approach with rising popularity in analyzing time-dependent problems in science and engineering is the so-called space-time finite-element method that utilized finiteelements in both space and time. A common ansatz in this context is to…
In this paper we propose a novel and general approach to design semi-implicit methods for the simulation of fluid-structure interaction problems in a fully Eulerian framework. In order to properly present the new method, we focus on the…
The discrete fracture model (DFM) has been widely used in the simulation of fluid flow in fractured porous media. Traditional DFM uses the so-called hybrid-dimensional approach to treat fractures explicitly as low-dimensional entries (e.g.…
Owing to additive manufacturing techniques, a structure at millimeter length scale (macroscale) can be produced by using a lattice substructure at micrometer length scale (microscale). Such a system is called a metamaterial at the…
This paper presents a new stochastic finite element method for computing structural stochastic responses. The method provides a new expansion of stochastic response and decouples the stochastic response into a combination of a series of…
We consider a mixed finite element method for approximating the solution of nearly incompressible elasticity and Stokes equations. The finite element method is based on quadrilateral and hexahedral triangulation using primal and dual…
We propose a finite element method for simulating one-dimensional solid models moving and experiencing large deformations while immersed in generalized Newtonian fluids. The method is oriented towards applications involving microscopic…
We describe a fully discrete mixed finite element method for the linearized rotating shallow water model, possibly with damping. While Crank-Nicolson time-stepping conserves energy in the absence of drag or forcing terms and is not subject…
Lightweight, single-use explosion containment structures provide an effective solution for neutralizing rogue explosives, combining affordability with ease of transport. This paper introduces a three-stage simulation framework that captures…
In computational engineering, ensuring the integrity and safety of structures in fields such as aerospace and civil engineering relies on accurate stress prediction. However, analytical methods are limited to simple test cases, and…
We develop a novel finite element method for a phase field model of nematic liquid crystal droplets. The continuous model considers a free energy comprised of three components: the Ericksen's energy for liquid crystals, the Cahn-Hilliard…
In this work, we propose a novel formulation for the solution of partial differential equations using finite element methods on unfitted meshes. The proposed formulation relies on the discrete extension operator proposed in the aggregated…
A novel method for complex fluid-structure interaction (FSI) involving large structural deformation and motion is proposed. The new approach is based on a hybrid fluid formulation that combines the advantages of purely Eulerian (fixed-grid)…
This paper presents a decentralized methodology for detecting and mitigating flapping phenomena in power systems, primarily caused by the operation of discrete devices. The proposed approach applies moving-window autocorrelation to local…
A probabilistic approach to phase-field brittle and ductile fracture with random material and geometric properties is proposed within this work. In the macroscopic failure mechanics, materials properties and exactness of spatial quantities…