CastLab: an object-oriented finite element toolbox within the Matlab environment for educational and research purposes in computational solid mechanics

This paper presents a kinematic enhanced plate model formulated within the Mindlin-Reissner theory. The main purpose of the model is to simulate the behavior of a structure up to membrane or bending failure. The shear strain is taken into account and the numerical shear locking problem is regularized by the Assumed Transverse Shear strain Field method. Two kinematic enhancements are applied at the level of the displacement fields by introducing two strong discontinuity fields. The first one is associated with the membrane displacement field and allows to describe the membrane failure and the second one is introduced in the rotation field to describe the bending failure. The Embedded Finite Element Method is used to incorporate the two kinematic discontinuities within a plate finite element, which allows to determine these new variables at the local level by the static condensation technique and to keep the architecture of the computational software unchanged. The kinematic and equilibrium operators associated with the enhancement variables are determined by fulfilling specific conditions. Case-studies are considered to asses the relevancy of the behavior of the enhanced membrane component as well as the behavior of the enhanced bending component. A mesh sensitivity analysis is also carried out. Finally, the Willam's test is performed for both components to verify the numerical robustness of the model and to analyze the apparent anisotropy associated with the development of discontinuities within the element. The present results allow to demonstrate the robustness of the numerical framework reported in this paper.

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“…Hy! (15) In order to obtain a generalized form of the plate behavior, the generalized force equations (10)…”

Section: S Z_mentioning

confidence: 99%

“…The test is performed for both membrane and rotation discontinuities. The numerical implementations as well as the various cases studied were carried out in CastLab toolbox [10].…”

Section: Introductionmentioning

confidence: 99%

Mindlin-Reissner plate formulation with enhanced kinematics: Theoretical framework and numerical applications

Bitar

Richard

2020

Engineering Fracture Mechanics

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“…Such problem can be, however, restated in a different way. Indeed, since ∆τ > 0, fulfilling conditions (54) implies that f α (e k+1 α , κ k+1 α ) = 0 for any dissipative process such that ∆κ k+1 α = ∆τ . As a consequence, increments δλ k+1 α can be equivalently computed from:…”

Section: Loading Factor Variation δλmentioning

confidence: 99%

“…They consist in imposing the increment of the linear combination of selected global DOFs (GS-CNDI, Control by Nodal Displacement Increment [6]) and the maximal strain variation over the domain (GS-CMSI, Control by Maximal Strain Increment [8,9,10]). Numerical developments were performed using the "CastLab" toolbox [54].…”

Section: Numerical Test Casesmentioning

confidence: 99%

Discontinuity-scale path-following methods for the embedded discontinuity finite element modeling of failure in solids

Rastiello¹,

Riccardi²,

Richard

2019

Computer Methods in Applied Mechanics and Engineering

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The initiation and propagation of cracks in solids often leads to unstable structural responses characterized by snap-backs. Path-following procedures allow finding a solution to the algebraic system of equations resulting from the numerical formulation of the considered problem. Accordingly, the boundary value problem is supplemented by a novel global unknown, namely, the loading factor, which should comply with a dedicated equation, the so-called path-following constraint equation. In this contribution, path-following methods are discussed within the framework of the Embedded Finite Element Method (E-FEM). Thanks to the enhanced kinematic description provided by the E-FEM, we show that it is possible to formulate constraint equations where the prescribed quantities are directly related to the dissipative process occurring at the strong discontinuity level. After introducing the augmented E-FEM formulation, three discontinuity-scale path-following constraints and their numerical implementation (using an operator-splitting method) are described. Simple quasi-static strain localization problems characterized by unstable structural responses exhibiting multiple snap-backs are numerically simulated. A comparison with several well-known constraint equations (commonly used in non-linear finite element computations) is finally established. This allows for illustrating the main features of the proposed methods as well as their efficiency in controlling highly unstable embedded discontinuity finite element simulations.

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“…Thus, they are not suitable for the visualization of flow phenomena in porous media at the undergraduate level. On the other hand, mathematical software like MATLAB [17], which is easily accessible and commonly applied in some general engineering undergraduate courses like calculus, is more suitable for visualized instruction of Flow in Porous Media for undergraduates [65] because the toolbox in the MATLAB platform known as "pdetool" [11,41] provides a graphical user interface (GUI) for solving general partial differential equations (PDEs); thus, the effect of the second challenge in the instruction of Flow in Porous Media (aforementioned) will be simultaneously mitigated.…”

Section: Introductionmentioning

confidence: 99%

An integrated numerical visualization teaching approach for an undergraduate course, Flow in Porous Media: An attempt toward sustainable engineering education

Okere

et al. 2021

Comp Applic In Engineering

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The complexities of observing flow phenomena in porous media have made it difficult to teach the course, Flow in Porous Media, to undergraduate students majoring in petroleum engineering. In this study, we propose an integrated numerical visualization teaching (INVT) approach that is based on MATLAB Pdetool, graphical user interface, and Visual Basic Programming. The effectiveness of the INVT method was evaluated in two ways: First, via statistical analyses of the examination grades of two groups (experimental and control groups) of selected undergraduate students from the school of petroleum engineering, after a carefully designed INVT tutorial program was conducted on the experimental group, and

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CastLab: an object-oriented finite element toolbox within the Matlab environment for educational and research purposes in computational solid mechanics

Cited by 11 publications

References 31 publications

Mindlin-Reissner plate formulation with enhanced kinematics: Theoretical framework and numerical applications

Mindlin-Reissner plate formulation with enhanced kinematics: Theoretical framework and numerical applications

Discontinuity-scale path-following methods for the embedded discontinuity finite element modeling of failure in solids

An integrated numerical visualization teaching approach for an undergraduate course, Flow in Porous Media: An attempt toward sustainable engineering education

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