On the effect of constraint parameters on the generalized displacement control method

Leon, Sofie E.; Lages, Eduardo Nobre; Araújo, Catarina N. de; Paulino, Gláucio H.

doi:10.1016/j.mechrescom.2013.12.009

Cited by 35 publications

(19 citation statements)

References 15 publications

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“…Thus, to achieve a successful nonlinear analysis of the structure, we need a suitable solution scheme. Here, we use the modified generalized displacement control method (MGDCM) [48], a variant of arc-length methods, as the solver. The MGDCM method has shown its advantages in tracking complicated solution paths of nonlinear problems compared to the standard generalized displacement control method (GDCM) [49].…”

Section: A Solution Scheme For Nonlinear Analysismentioning

confidence: 99%

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Nonlinear mechanics of non-rigid origami: an efficient computational approach

2017

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Origami-inspired designs possess attractive applications to science and engineering (e.g. deployable, self-assembling, adaptable systems). The special geometric arrangement of panels and creases gives rise to unique mechanical properties of origami, such as reconfigurability, making origami designs well suited for tunable structures. Although often being ignored, origami structures exhibit additional soft modes beyond rigid folding due to the flexibility of thin sheets that further influence their behaviour. Actual behaviour of origami structures usually involves significant geometric nonlinearity, which amplifies the influence of additional soft modes. To investigate the nonlinear mechanics of origami structures with deformable panels, we present a structural engineering approach for simulating the nonlinear response of non-rigid origami structures. In this paper, we propose a fully nonlinear, displacement-based implicit formulation for performing static/quasi-static analyses of non-rigid origami structures based on 'bar-and-hinge' models. The formulation itself leads to an efficient and robust numerical implementation. Agreement between real models and numerical simulations demonstrates the ability of the proposed approach to capture key features of origami behaviour.

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Section: A Solution Scheme For Nonlinear Analysismentioning

confidence: 99%

“…end while 13: end for to poor convergence. However, the MGDCM is not very sensitive to the value of the initial load factor, which means that we can get convergent solutions for a relatively wide range of λ [48].…”

Section: A Solution Scheme For Nonlinear Analysismentioning

confidence: 99%

Nonlinear mechanics of non-rigid origami: an efficient computational approach

2017

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“…Generalized displacement control method has been proposed as an alternative method to follow loading path, which already shows great potential for complex nonlinear problems. Recently, a modification of GDCM (MGDCM) method is proposed, which presents more robust performance and ability to capture equilibrium paths with high curvature. In this paper, MGDCM path‐following algorithm is adopted to trace load‐displacement curves. Stability points are important concepts closely related to energy dissipation ability of unit cell.…”

Section: Large Deformation Topology Optimization Problemmentioning

confidence: 99%

A Heaviside function‐based density representation algorithm for truss‐like buckling‐induced mechanism design

Deng

2019

Numerical Meth Engineering

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Summary Motivated by key advances in manufacturing techniques, the tailoring of materials to achieve novel properties such as energy dissipation properties has been the focus of active research in engineering and materials science over the past decade. The goal of material design is to determine the optimal spatial layout to achieve a desired macroscopic constitutive response. However, the manufacturing abilities are the key factors to constrain the feasible design space, eg, minimum length and geometry complexity. Traditional density‐based method, where each element works as a variable, always results in complicated geometry with large number of small intricate features. To address the aforementioned challenges, a new density field representation technique, named, Heaviside function‐based geometric representation algorithm, is proposed in this paper, where density field is represented by truss‐like components. Truss‐like components have less control parameters and easier to handle for sensitivities derivation, especially for distance sensitivities. Using bar components to explicitly represent density field can explore design space effectively and generate simple structures without any intricate small features at borders. Furthermore, this density representation method is mesh independent and design variables are reduced significantly so that optimization problem can be solved efficiently using small‐scale optimization algorithm, eg, sequential quadratic programming. However, finding a reasonable initial component distribution is critical to avoid optimization failure. To overcome this difficulty, a jump‐start method is proposed by solving inverse subproblem. The overall optimization progress is divided into three stages, ie, the first stage is obtaining coarse snap‐through material configuration based on traditional density‐based method; the second stage is an inverse optimization problem to fit the geometry component to the solution obtained in stage I; and the stage III is maximizing the energy dissipation capacity. To demonstrate the powerful ability in design buckling‐induced mechanism of the proposed density representation algorithm, buckling‐induced energy dissipation mechanism with snap‐through behavior to achieve the desired energy dissipation capacity considering failure constraint is demonstrated through four numerical examples.

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“…Due to its characteristic nonlinear behavior with consecutive variations in the loading direction, this structure has regularly been used to investigate nonlinear solution schemes. 8,18,[42][43][44] Three vertical downward loads are applied to the three top nodes, where the magnitude of the loads applied on the side nodes is one and a half times the load applied on the middle node. The axial stiffness in each bar is EA = 1.0.…”

Section: Twelve Bar Trussmentioning

confidence: 99%

A stiffness parameter and truncation error criterion for adaptive path following in structural mechanics

Maghami

Schillinger

2019

Numerical Meth Engineering

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Summary We explore a truncation error criterion to steer adaptive step length refinement and coarsening in incremental‐iterative path following procedures, applied to problems in large‐deformation structural mechanics. Elaborating on ideas proposed by Bergan and collaborators in the 1970s, we first describe an easily computable scalar stiffness parameter whose sign and rate of change provide reliable information on the local behavior and complexity of the equilibrium path. We then derive a simple scaling law that adaptively adjusts the length of the next step based on the rate of change of the stiffness parameter at previous points on the path. We show that this scaling is equivalent to keeping a local truncation error constant in each step. We demonstrate with numerical examples that our adaptive method follows a path with a significantly reduced number of points compared to an analysis with uniform step length of the same fidelity level. A comparison with Abaqus illustrates that the truncation error criterion effectively concentrates points around the smallest‐scale features of the path, which is generally not possible with automatic incrementation solely based on local convergence properties.

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On the effect of constraint parameters on the generalized displacement control method

Cited by 35 publications

References 15 publications

Nonlinear mechanics of non-rigid origami: an efficient computational approach

Nonlinear mechanics of non-rigid origami: an efficient computational approach

A Heaviside function‐based density representation algorithm for truss‐like buckling‐induced mechanism design

A stiffness parameter and truncation error criterion for adaptive path following in structural mechanics

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