SCS: A one‐dimensional piecewise‐linear large strain consolidation model for structured soils

2021 ◽  
Author(s):  
Ji Sen Shi ◽  
Dao Sheng Ling ◽  
Jia Jun Niu
Keyword(s):  
Large Strain ◽  
Piecewise Linear ◽  
One Dimensional ◽  
Structured Soils ◽  
Consolidation Model

CONTINUOUS PIECEWISE LINEAR FUNCTIONS

2005 ◽  
Vol 10 (1) ◽  
pp. 77-99 ◽  
Author(s):  
CHARALAMBOS D. ALIPRANTIS ◽  
DAVID HARRIS ◽  
RABEE TOURKY
Keyword(s):  
Piecewise Linear ◽  
Continuous Functions ◽  
Linear Functions ◽  
Dimensional Euclidean Space ◽  
Piecewise Linear Functions ◽  
Space Of Continuous Functions ◽  
One Dimensional ◽  
Mathematical Background ◽  
Linear Regressions ◽  
Special Case

The paper studies the function space of continuous piecewise linear functions in the space of continuous functions on them-dimensional Euclidean space. It also studies the special case of one dimensional continuous piecewise linear functions. The study is based on the theory of Riesz spaces that has many applications in economics. The work also provides the mathematical background to its sister paper Aliprantis, Harris, and Tourky (2006), in which we estimate multivariate continuous piecewise linear regressions by means of Riesz estimators, that is, by estimators of the the Boolean formwhereX=(X1,X2, …,Xm) is some random vector, {Ej}j∈Jis a finite family of finite sets.

A FDM Solving Method of Large-Strain Consolidation of Multi-Layers Super Soft-Soil

2011 ◽  
Vol 71-78 ◽  
pp. 1880-1884
Author(s):  
Hai Jia Wen ◽  
Jia Lan Zhang
Keyword(s):  
Numerical Method ◽  
Large Strain ◽  
Soft Soil ◽  
Focal Points ◽  
One Dimensional ◽  
Practical Engineering ◽  
K Function ◽  
Soil Foundation ◽  
Soft Soil Foundation ◽  
The One

The aim is to present a numerical method to solve the large-strain consolidation of super soft-soil. The theory of large-strain consolidation (LSC) is acted as the better method for analysis on the consolidation problem of super soft-soil foundation. The focal points are, based on practical engineering, the one-dimensional LSC equations being derived, the consolidation coefficients being inquired and so on. Based on these, one-dimensional nonlinear LSC equation is solved by the FDM, the e~p and e~k function that are according with the practical engineering is introduced into the solving progress, and the multi-layers super soft-soil is also considered in the progress successfully etc. Finally, a case showed the satisfied analysis result by LSCFDM. And some realizations about LSC analysis on super soft-soil are concluded.

COMBINING ADJOINT STABILIZED METHODS FOR THE ADVECTION-DIFFUSION-REACTION PROBLEM

2007 ◽  
Vol 17 (02) ◽  
pp. 305-326 ◽  
Author(s):  
GUILLERMO HAUKE ◽  
GIANCARLO SANGALLI ◽  
MOHAMED H. DOWEIDAR
Keyword(s):  
Piecewise Linear ◽  
Diffusion Reaction ◽  
One Dimensional ◽  
Stabilized Methods ◽  
Advection Diffusion ◽  
Diffusive Limit ◽  
Reaction Transport ◽  
Globally Stable ◽  
Supg Method ◽  
Reaction Problem

Computational methods for the advection-diffusion-reaction transport equation are still a challenge. Although there exist globally stable methods, oscillations around sharp layers such as boundary, inner and outflow layers, are typical in multi-dimensional flows. In this paper a variational formulation that combines two types of stabilization integrals is proposed, namely an adjoint stabilization and a gradient adjoint stabilization. Two free parameters are chosen by imposing one-dimensional superconvergence. Then, when applied to multi-dimensional flows, the method presents better local stability than the present stabilized methods. Furthermore, in the advective-diffusive limit and for piecewise linear functional spaces, the method recovers the classical SUPG method.

Nonlocality of one-dimensional bilinear hardening–softening elastoplastic axial lattices

2019 ◽  
Vol 25 (2) ◽  
pp. 475-497
Author(s):  
Vincent Picandet ◽  
Noël Challamel
Keyword(s):  
Difference Equations ◽  
Differential Operators ◽  
Scale Effects ◽  
Piecewise Linear ◽  
Three Dimensional ◽  
Continuous Model ◽  
Lattice System ◽  
Discrete Problem ◽  
Linear Difference Equations ◽  
One Dimensional

The static behaviour of an elastoplastic axial lattice is studied in this paper through both discrete and nonlocal continuum analyses. The elastoplastic lattice system is composed of piecewise linear hardening–softening elastoplastic springs connected between each other via nodes, loaded by concentrated tension forces. This inelastic lattice evolution problem is ruled by some difference equations, which are shown to be equivalent to the finite difference formulation of a continuous elastoplastic bar problem under distributed tension load. Exact solutions of this inelastic discrete problem are obtained from the resolution of this piecewise linear difference equations system. Localization of plastic strain in the first elastoplastic spring, connected to the fixed end, is observed in the softening range. A continuous nonlocal elastoplastic theory is then built from the lattice difference equations using a continualization process, based on a rational asymptotic expansion of the associated pseudo-differential operators. The continualized lattice-based model is equivalent to a distributed nonlocal continuous elastoplastic theory coupled to a cohesive elastoplastic model, which is shown to capture efficiently the scale effects of the reference axial lattice. The hardening–softening localization process of the nonlocal elastoplastic continuous model strongly depends on the lattice spacing, which controls the size of the nonlocal length scales. An analogy with the one-dimensional lattice system in bending is also shown. The considered microstructured elastoplastic beam is a Hencky bar-chain connected by elastoplastic rotational springs. It is shown that the length scale calibration of the nonlocal model strongly depends on the degree of the difference equations of each lattice model (namely axial or bending lattice). These preliminary results valid for one-dimensional systems allow possible future developments of new nonlocal elastoplastic models, including two- or even three-dimensional elastoplastic interactions.

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