FDM and FEM solutions to linear dynamics of porous media: stabilised, monolithic and fractional schemes

Numerical Meth Engineering

Pedroso

et al. 2017

Self Cite

Summary This paper presents a strategy to improve the efficiency of simulations involving porous materials with linear behaviour and full saturation. The method is named parallel‐lines finite difference and uses a method to decouple a discretised version of the governing equations allowing parallel computations. As a result, the complexity and the bandwidth of the global matrix are significantly reduced and hence the efficiency is improved. The other advantage of the scheme is the fulfilment of the inf‐sup stability condition. The scheme is developed to solve porous media formulations derived from the theory of porous media. Both the u‐p and u‐v‐p formulations are considered (u: displacement of solid, p: pressure of liquid, and v: velocity of liquid). Several simulations are performed to demonstrate the capabilities of the method.

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

\frac{\partial^{2}}{\partial x^{2}}

\frac{\partial^{2}}{\partial y^{2}}

, and

\frac{\partial^{2}}{\partial z^{2}}

) into 3 parts, each one containing the other derivative as an implicit function. In this way, the global matrix of the resulting linear system of equations becomes much simpler.…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

FDM solutions to linear dynamics of porous media: Efficiency, stability, and parallel solution strategy

Numerical Meth Engineering

Pedroso

et al. 2017

Self Cite

One‐dimensional dynamics of saturated incompressible porous media: analytical solutions and influence of inertia terms

Num Anal Meth Geomechanics

Pedroso

Ehlers

2016

Self Cite

SUMMARYThe complexity of formulations for the hydromechanical coupled mechanics of porous media is typically minimised by simplifying assumptions such as neglecting the effect of inertia terms. For example, three formulations commonly employed to model practical problems are classified as fully dynamic, simplified dynamic and quasi-static. Thus, depending on the porous media conditions, each formulation will have advantages and limitations. This paper presents a comprehensive analysis of these limitations when solving one-dimensional fully saturated porous media problems in addition to a new solution that considers a more general loading situation. A phase diagram is developed to assist on the selection of which formulation is more appropriate and convenient regarding particular cases of porosity and hydraulic conductivity values. Non-dimensional formulations are proposed to achieve this goal. Results using the analytical solutions are compared against numerical values obtained with the finite element method, and the effect of porosity is investigated.

Optimal design of functionally graded lattice structures using Hencky bar-grid model and topology optimization

Wang

Challamel

et al. 2022

Struct Multidisc Optim

Presented herein is a novel design framework for obtaining the optimal design of functionally graded lattice (FGL) structures that involve using a physical discrete structural model called the Hencky bar-grid model (HBM) and topology optimization (TO). The continuous FGL structure is discretized by HBM comprising rigid bars, frictionless hinges, frictionless pulleys, elastic primary and secondary axial springs, and torsional springs. A penalty function is introduced to each of the HBM spring’s stiffnesses to model non-uniform material properties. The gradient-based TO method is applied to find the stiffest structure via minimizing the compliance or elastic strain energy by adjusting the HBM spring stiffnesses subjected to prescribed design constraints. The optimal design of FGL structures is constructed based on the optimal spring stiffnesses of the HBM. The proposed design framework is simple to implement and for obtaining optimal FGL structures as it involves a relatively small number of design variables such as the spring stiffnesses of each grid cell. As illustration of the HBM-TO method, some optimization problems of FGL structures are considered and their optimal solutions obtained. The solutions are shown to converge after a small number of iterations. A Python code is given in the Appendix for interested readers who wish to reproduce the results.