Exploring the design space of nonlinear shallow arches with generalised path-following

Cox, Bradley; Groh, Rainer; Avitabile, Daniele; Pirrera, Alberto

doi:10.1016/j.finel.2018.01.004

Cited by 16 publications

(3 citation statements)

References 38 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…As such, many recent proposals move in this direction. This goal is reached, for instance, through the use of efficient solution algorithms, like in Koiter, 4‐6 Koiter–Newton approaches, 7,8 and in generalized path following methods 9,10 . Conversely, the reduction of the discrete variables is pursued, among the others, by the isogeometric formulations 11,12 that take advantage from the high continuity of interpolation functions, and by high‐performing finite elements (FE) 13,14 .…”

Section: Introductionmentioning

confidence: 99%

A corotational mixed flat shell finite element for the efficient geometrically nonlinear analysis of laminated composite structures

Liguori

Madeo

2021

Numerical Meth Engineering

View full text Add to dashboard Cite

A corotational flat shell element for the geometrically nonlinear analysis of laminated composite structures is presented. The element is obtained from the Hellinger–Reissner variational principle with assumed stress and displacement fields. The stress interpolation is derived from the linear elastic solution for symmetric composite materials. The element is isostatic, namely the stress interpolation is ruled by the minimum number of parameters. Displacement and rotation fields are only assumed along the contour of the element. As such, all the operators are efficiently obtained through analytical contour integration. The geometrical nonlinearity is introduced by means of a corotational formulation. The proposed finite element, named MISS‐4c, proves to be locking free and shows no rank defectiveness. A multimodal Koiter's algorithm is used to obtain the initial postbuckling response. Results show good accuracy and high convergence rate in the geometrically nonlinear analysis of composite shell structures.

show abstract

Section: Introductionmentioning

confidence: 99%

A corotational mixed flat shell finite element for the efficient geometrically nonlinear analysis of laminated composite structures

Liguori

Madeo

2021

Numerical Meth Engineering

View full text Add to dashboard Cite

show abstract

“…Recently, with the advent of new materials and advanced numerical techniques, interest in postbuckling response of the nonlinear structures has arisen. 35 The use of light weight and thin-walled structure which can buckle, have long been avoided due to the fear of snap-through behaviour. However, now some researchers proposed the novel and innovative design which use the snap-through behaviour as a requirement in shape-morphing structures and mechanically multi-stable components.…”

Section: Introductionmentioning

confidence: 99%

In-plane nonlinear postbuckling analysis of circular arches using absolute nodal coordinate formulation with arc-length method

Shaukat

Peng

Wang

et al. 2020

Proceedings of the Institution of Mechanical Engineers, Part K:

View full text Add to dashboard Cite

In this study, Absolute Nodal Coordinate Formulation (ANCF) in conjunction with Crisfield’s arc-length method is utilized in order to predict the nonlinear postbuckling behaviour of circular arches. The whole primary equilibrium path in load-displacement space of circular arches under central concentrated load is obtained. Three ANCF based approaches, i.e., the conventional two-dimensional fully parameterized shear deformable ANCF beam element based on the General Continuum Mechanics (GCM) approach, the same element modified by the Strain Split Method (SSM) approach and the ANCF planar Higher Order Beam Element (HOBE) with GCM approach are used. Circular arches with various geometric configurations and boundary conditions such as clamped-clamped, hinged-hinged, clamped-hinged and three-hinged arches are studied which exhibit nonlinear response in the form of snap-through, snap-back and looping phenomenon. The obtained results are compared with the analytical solutions, experimental result (where available in the literature) and numerical approximations (by using the commercially available FEM package). In this paper, the recently proposed ANCF based approaches are successfully implemented which validate and verify the utility of ANCF in nonlinear postbuckling analysis. The characteristics of the three approaches with regard to the adoptability of arc-length method are compared and discussed.

show abstract

“…In the present work, it has been considered most appropriate to use the term sequence for the set of calculated individual equilibrium states, not to over-emphasize an assumed continuity between the states. This notation is thereby also relevant for evaluations of the variations in structural response, when the structure is parameterized in geometry or properties [12]. A particular setting is then when forces on a structure are multi-parametric, for instance, when the coupling between gas pressure and electrical activation can create unusual instability situations [34].…”

Section: Introductionmentioning

confidence: 99%

Constrained stability of conservative static equilibrium

Eriksson

Nordmark

2019

Comput Mech

View full text Add to dashboard Cite

Modelling of static structural stability problems is considered. Focus is set on problems where passive physical constraints affect the response to applied forces, and where more than one free parameter describes the setting. The existence of vibration frequencies at equilibrium states is investigated, as an indication of stability. The relevant Jacobian matrix is developed, with an emphasis on the necessity to formulate the constraint equations from an energy form in a conservative problem. The corresponding mass matrix is introduced, with zero mass contribution from constraint equations. Three different forms of the relevant Jacobians are considered, and alternative methods for the eigenvalue extraction given. Stability is discussed in a context of generalized equilibrium problems, where auxiliary parameters and equations can be included in a continuation setting. Examples show the formulation, implementation and interpretation of stability.

show abstract

Exploring the design space of nonlinear shallow arches with generalised path-following

Cited by 16 publications

References 38 publications

A corotational mixed flat shell finite element for the efficient geometrically nonlinear analysis of laminated composite structures

A corotational mixed flat shell finite element for the efficient geometrically nonlinear analysis of laminated composite structures

In-plane nonlinear postbuckling analysis of circular arches using absolute nodal coordinate formulation with arc-length method

Constrained stability of conservative static equilibrium

Contact Info

Product

Resources

About