Related papers: Optimal fine-scale structures in compliance minimi…
A highly deformable rod, modelled as the extensible elastica, is connected to a movable clamp at one end and to a pin sliding along a frictionless curved profile at the other. Bifurcation analysis shows that axial compliance provides a…
This paper introduces a heuristic topology optimization framework for thin-walled, 2D extruded lattice structures subject to complex high-speed loading. The proposed framework optimizes the wall thickness distribution in the lattice cross…
The three dimensional optimal energy growth mechanism, in plane parallel shear flows, is reexamined in terms of the role of vortex stretching and the interplay between the span-wise vorticity and the planar divergent components. For high…
In this note, we propose a formal framework accounting for the sensitivity of a function of the domain with respect to the addition of a thin ligament. To set ideas, we consider the model setting of elastic structures, and we approximate…
We propose an efficient probabilistic method to solve a deterministic problem -- we present a randomized optimization approach that drastically reduces the enormous computational cost of optimizing designs under many load cases for both…
Influence of uniaxial small-scale anisotropy and compressibility on the stability of scaling regime and on the anomalous scaling of structure functions of a scalar field is investigated in the model of a passive scalar field advected by the…
The increasing availability of full-field displacement data from imaging techniques in experimental mechanics is determining a gradual shift in the paradigm of material model calibration and discovery, from using several simple-geometry…
Uniform flow distribution across parallel channels directly impacts the performance and efficiency of many fluid and energy systems. However, designing efficient flow manifolds that ensure uniform flow distribution remains a challenge. This…
We discover unified scaling laws for the mean wall shear stress and the mean velocity profile in turbulent boundary layers subject to favorable and adverse mean pressure gradients-including flows with separation and reattachment. We use the…
We present a general numerical approach to shape optimization with state constraints for 2-dimensional geometries, without relaxing the constraints. To do this we reformulate the problem on a fixed reference domain using a conformal…
We study optimal design problems involving variational inequalities with unilateral conditions in the domain and pointwise boundary observation. We use regularizing and penalization tehniques in the setting of the Hamiltonian approach to…
This paper proposes a computational framework for the design optimization of stable structures under large deformations by incorporating nonlinear buckling constraints. A novel strategy for suppressing spurious buckling modes related to…
The paper shows an inf-sup stability property for several well-known 2D and 3D Stokes elements on triangulations which are not fitted to a given smooth or polygonal domain. The property implies stability and optimal error estimates for a…
Static friction induced by moir\'e superstructure in twisted incommensurate finite layered material interfaces reveals unique double periodicity and lack of scaling with contact size. The underlying mechanism involves compensation of…
Dynamical PDEs that have a spatial divergence form possess conservation laws that involve an arbitrary function of time. In one spatial dimension, such conservation laws are shown to describe the presence of an $x$-independent source/sink;…
A (unit norm) frame is scalable if its vectors can be rescaled so as to result into a tight frame. Tight frames can be considered optimally conditioned because the condition number of their frame operators is unity. In this paper we…
We study the finite-size scaling behaviour at the critical point, resulting from the addition of a homogeneous size-dependent perturbation, decaying as an inverse power of the system size. The scaling theory is first formulated in a general…
This work comprises a detailed theoretical and computational study of the boundary value problem for transversely isotropic linear elastic bodies. General conditions for well-posedness are derived in terms of the material parameters. The…
Topology optimization is used for the design of high-performance structures but remains fundamentally limited by its iterative nature, requiring repeated finite element analyses that prevent real-time deployment and large-scale design…
This paper presents an algorithm for reliability-based topology optimization of linear elastic continua under random-field material model. The modelling random field is discretized into a small number of random variables, and then the…