SHUGUANG LI's Outputs (40)

A multi-scale uncertainty quantification model encompassing minimum-size unit cells for effective properties of plain woven composites (2024)
Journal Article
Yang, Y.-C., Gou, J.-J., Gong, C.-L., Sun, Y.-E., & Li, S. (2024). A multi-scale uncertainty quantification model encompassing minimum-size unit cells for effective properties of plain woven composites. Composite Structures, Article 118648. https://doi.org/10.1016/j.compstruct.2024.118648

The uncertainty quantification is crucial to the high-precision prediction of composites’ effective properties. However, the unclear input uncertainties of multiscale parameters, complex uncertainty propagations of inter-scale correlations, and unaff... Read More about A multi-scale uncertainty quantification model encompassing minimum-size unit cells for effective properties of plain woven composites.

Unveiling the deformability of mussel plaque core: the role of pore distribution and hierarchical structure (2024)
Journal Article
Lyu, Y., Tan, M., Pang, Y., Sun, W., Li, S., & Liu, T. (2024). Unveiling the deformability of mussel plaque core: the role of pore distribution and hierarchical structure. Soft Matter, 20(37), 7405-7419. https://doi.org/10.1039/d4sm00832d

The mussel thread-plaque system exhibits strong adhesion and high deformability, allowing it to adhere to various surfaces. While the microstructure of plaques has been thoroughly studied, the effect of their unique porous structure on the high defor... Read More about Unveiling the deformability of mussel plaque core: the role of pore distribution and hierarchical structure.

Validation of the fully rationalized Tsai-Wu failure criterion for unidirectional laminates under multiaxial stress states through a ring-on-ring test (2024)
Journal Article
Li, J., Yan, S., Kong, W., & Li, S. (2024). Validation of the fully rationalized Tsai-Wu failure criterion for unidirectional laminates under multiaxial stress states through a ring-on-ring test. Composites Science and Technology, 257, Article 110813. https://doi.org/10.1016/j.compscitech.2024.110813

Validating a failure criterion under complex stress states is important because composites often encounter multiaxial stress in practical applications, but it also helps to expose any deficiencies of the criterion in failure prediction in the presenc... Read More about Validation of the fully rationalized Tsai-Wu failure criterion for unidirectional laminates under multiaxial stress states through a ring-on-ring test.

Stress or strain? (2024)
Journal Article
Li, S. (2024). Stress or strain?. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 480(2295), Article 20240269. https://doi.org/10.1098/rspa.2024.0269

This article is intended to reconcile the stress-based and strain-based formulations for material failure criteria, where a long-standing and deep division is present. The two approaches do not naturally agree with each other, and they do not genuine... Read More about Stress or strain?.

Characterisation of 3D woven textile composites in presence of minor weft tow undulations and cross-section variations (2024)
Journal Article
Xu, M., Sitnikova, E., Kong, W., Zhang, J., Hu, S., & Li, S. (2024). Characterisation of 3D woven textile composites in presence of minor weft tow undulations and cross-section variations. Journal of Composite Materials, 58(25), 2671-2691. https://doi.org/10.1177/00219983241270939

Weft tows in 3D woven composites are commonly approximated as perfectly straight, but their undulations are inevitable in reality, although the extent of undulations in the weft tows is not as pronounced as in the warp tows. Such minor undulations in... Read More about Characterisation of 3D woven textile composites in presence of minor weft tow undulations and cross-section variations.

Stress Invariants and Invariants of the Failure Envelope as a Quadric Surface: Their Significances in the Formulation of a Rational Failure Criterion (2024)
Journal Article
Li, S. (2024). Stress Invariants and Invariants of the Failure Envelope as a Quadric Surface: Their Significances in the Formulation of a Rational Failure Criterion. Mechanics of Materials, 196, Article 105076. https://doi.org/10.1016/j.mechmat.2024.105076

When stress invariants up to the second order are employed to construct failure criterion for brittle materials, it involves three independent terms and therefore there are three coefficients to be determined. However, there are only two conditions a... Read More about Stress Invariants and Invariants of the Failure Envelope as a Quadric Surface: Their Significances in the Formulation of a Rational Failure Criterion.

Rational implementation of the Mohr criterion in its general form (2024)
Journal Article
Li, S. (2024). Rational implementation of the Mohr criterion in its general form. International Journal of Mechanical Sciences, 279, 109449. https://doi.org/10.1016/j.ijmecsci.2024.109449

The Mohr criterion is successfully implemented for brittle materials in its general form based on failure envelopes formulated using quadratic functions. This is probably the first time when the criterion has been made comprehensive enough and yet co... Read More about Rational implementation of the Mohr criterion in its general form.

A failure criterion for genuinely orthotropic materials and integration of a series of criteria for materials of different degrees of anisotropy (2024)
Journal Article
Xu, M., Sitnikova, E., & Li, S. (2024). A failure criterion for genuinely orthotropic materials and integration of a series of criteria for materials of different degrees of anisotropy. Royal Society Open Science, 11(5), Article 240205. https://doi.org/10.1098/rsos.240205

Existing failure criteria for orthotropic materials are subject to an underlying assumption which cause contradictions when applied to genuinely orthotropic materials that are significantly anisotropic in elasticity as well as in strengths. For such... Read More about A failure criterion for genuinely orthotropic materials and integration of a series of criteria for materials of different degrees of anisotropy.

An inverse application of unit cells for extracting fibre properties from effective properties of composites (2023)
Journal Article
Zou, Z., & Li, S. (2023). An inverse application of unit cells for extracting fibre properties from effective properties of composites. Mathematics and Mechanics of Solids, https://doi.org/10.1177/10812865231212150

A semi-analytical solution is obtained in this paper for the micromechanical analysis of the square and hexagonal unit cells using complex potentials. It provides a means of numerical characterisation of unidirectionally fibre-reinforced composites f... Read More about An inverse application of unit cells for extracting fibre properties from effective properties of composites.

A theoretical framework underlying an accelerated testing method and its application to composites under constant strain rates and fatigue loading (2022)
Journal Article
Xu, F., Arthur Jones, I., & Li, S. (2022). A theoretical framework underlying an accelerated testing method and its application to composites under constant strain rates and fatigue loading. Science and Engineering of Composite Materials, 29(1), 488-499. https://doi.org/10.1515/secm-2022-0012

A theoretical framework that underlies an accelerated testing method for unidirectional (UD) composites is proposed in this article, based on the continuum damage mechanics and time-temperature superposition. By the way of demonstration, it has been... Read More about A theoretical framework underlying an accelerated testing method and its application to composites under constant strain rates and fatigue loading.

Laminated beams/shafts of annular cross-section subject to combined loading (2022)
Journal Article
Li, S., Johnson, M. S., Sitnikova, E., Evans, R., & Mistry, P. J. (2023). Laminated beams/shafts of annular cross-section subject to combined loading. Thin-Walled Structures, 182(Part A), Article 110153. https://doi.org/10.1016/j.tws.2022.110153

A novel stress analysis method is developed for the efficient design of radially laminated annular beams/shafts subject to arbitrary load combinations. The analysis is conducted using classic laminate theory (CLT) in conjunction with a mechanics of m... Read More about Laminated beams/shafts of annular cross-section subject to combined loading.

Controllable parameters as the essential components in the analysis, manufacturing and design of 3D woven composites (2022)
Journal Article
Sitnikova, E., Xu, M., Kong, W., & Li, S. (2022). Controllable parameters as the essential components in the analysis, manufacturing and design of 3D woven composites. Composites Science and Technology, 230, Article 109730. https://doi.org/10.1016/j.compscitech.2022.109730

The comprehensive design feasibility for woven composites has been established by identifying the missing component in the design tool for these materials, the so-called controllable parameters. These are the parameters that are involved, directly or... Read More about Controllable parameters as the essential components in the analysis, manufacturing and design of 3D woven composites.

Fully rationalized Tsai-Wu failure criterion for transversely isotropic materials (2022)
Book Chapter
Li, S. (2022). Fully rationalized Tsai-Wu failure criterion for transversely isotropic materials. In S. W. Tsaï (Ed.), Double-Double: a new perspective in the manufacture and design of composites (173-206). Stanford & JEC

By examining the quadratic function of the original Tsai-Wu failure criterion for transversely isotropic materials from the perspective of analytic geometry, two of the troublesome coefficients associated with the interactive terms, one describing in... Read More about Fully rationalized Tsai-Wu failure criterion for transversely isotropic materials.

The Formulation of the Quadratic Failure Criterion for Transversely Isotropic Materials: Mathematical and Logical Considerations (2022)
Journal Article
Li, S., Xu, M., & Sitnikova, E. (2022). The Formulation of the Quadratic Failure Criterion for Transversely Isotropic Materials: Mathematical and Logical Considerations. Journal of Composites Science, 6(3), Article 82. https://doi.org/10.3390/jcs6030082

The quadratic function of the original Tsai–Wu failure criterion for transversely isotropic materials is re-examined in this paper. According to analytic geometry, two of the troublesome coefficients associated with the interactive terms—one between... Read More about The Formulation of the Quadratic Failure Criterion for Transversely Isotropic Materials: Mathematical and Logical Considerations.

Continuous fibre composite 3D printing with pultruded carbon/PA6 commingled fibres: Processing and mechanical properties (2022)
Journal Article
Zhuo, P., Li, S., Ashcroft, I., & Jones, I. A. (2022). Continuous fibre composite 3D printing with pultruded carbon/PA6 commingled fibres: Processing and mechanical properties. Composites Science and Technology, 221, Article 109341. https://doi.org/10.1016/j.compscitech.2022.109341

Continuous Fibre composite 3D printing (CF-3DP) technology is a newly developed Additive Manufacturing (AM) process. By employing continuous fibre as a reinforcement for the composite, the mechanical properties of the 3D printed part can be significa... Read More about Continuous fibre composite 3D printing with pultruded carbon/PA6 commingled fibres: Processing and mechanical properties.

Material extrusion additive manufacturing of continuous fibre reinforced polymer matrix composites: A review and outlook (2021)
Journal Article
Zhuo, P., Li, S., Ashcroft, I. A., & Jones, A. I. (2021). Material extrusion additive manufacturing of continuous fibre reinforced polymer matrix composites: A review and outlook. Composites Part B: Engineering, 224, Article 109143. https://doi.org/10.1016/j.compositesb.2021.109143

In recent years, three-dimensional printing (3DP) technology has developed to include composite materials. Most of the development to date in this area has involved particulate or short fibre reinforced composites, whilst continuous fibre printing re... Read More about Material extrusion additive manufacturing of continuous fibre reinforced polymer matrix composites: A review and outlook.

Material extrusion additive manufacturing of continuous fibre reinforced polymer matrix composites: A review and outlook (2021)
Journal Article
Zhuo, P., Li, S., Ashcroft, I. A., & Jones, A. I. (2021). Material extrusion additive manufacturing of continuous fibre reinforced polymer matrix composites: A review and outlook. Composites Part B: Engineering, 224, Article 109143. https://doi.org/10.1016/j.compositesb.2021.109143

In recent years, three-dimensional printing (3DP) technology has developed to include composite materials. Most of the development to date in this area has involved particulate or short fibre reinforced composites, whilst continuous fibre printing re... Read More about Material extrusion additive manufacturing of continuous fibre reinforced polymer matrix composites: A review and outlook.

Experimental evaluation and theoretical prediction of elastic properties and failure of C/C‐SiC composite (2021)
Journal Article
Shi, Y., Li, S., Sitnikova, E., Cepli, D., & Koch, D. (2022). Experimental evaluation and theoretical prediction of elastic properties and failure of C/C‐SiC composite. International Journal of Applied Ceramic Technology, 19(1), 7-21. https://doi.org/10.1111/ijac.13775

The paper presents experimental characterization and theoretical predictions of elastic and failure properties of continuous carbon fiber reinforced silicon carbide (C/C-SiC) composite fabricated by Liquid Silicon Infiltration (LSI). Its mechanical p... Read More about Experimental evaluation and theoretical prediction of elastic properties and failure of C/C‐SiC composite.

Parametric sizing study for the design of a lightweight composite railway axle (2021)
Journal Article
Mistry, P. J., Johnson, M. S., Li, S., Bruni, S., & Bernasconi, A. (2021). Parametric sizing study for the design of a lightweight composite railway axle. Composite Structures, 267, Article 113851. https://doi.org/10.1016/j.compstruct.2021.113851

The potential for lightweighting of railway axles was investigated to primarily reduce the unsprung mass of a rail vehicle. The reduction of unsprung mass equates to an overall lighter train which will help to reduce track damage, energy consumption... Read More about Parametric sizing study for the design of a lightweight composite railway axle.

On the objectivity of the nonlinear along-fibre shear stress–strain relationship for unidirectionally fibre-reinforced composites (2021)
Journal Article
Li, S., Xu, M., Yan, S., & Sitnikova, E. (2021). On the objectivity of the nonlinear along-fibre shear stress–strain relationship for unidirectionally fibre-reinforced composites. Journal of Engineering Mathematics, 127(1), https://doi.org/10.1007/s10665-021-10098-3

The nonlinear along-fibre shear stress–strain relationship for unidirectionally fibre-reinforced composites has been investigated in this paper aiming at its applications in general 3D stress conditions in a consistent manner. So far, such relationsh... Read More about On the objectivity of the nonlinear along-fibre shear stress–strain relationship for unidirectionally fibre-reinforced composites.

Representative Volume Elements and Unit Cells: Concepts, Theory, Applications and Implementation (2020)
Book
Li, S., & Sitnikova, E. (2020). Representative Volume Elements and Unit Cells: Concepts, Theory, Applications and Implementation. Elsevier/Woodhead Publishing. https://doi.org/10.1016/C2017-0-03559-0

Numerical methods to estimate material properties usually involve analysis of a representative volume element (RVE) or unit cell (UC). The representative volume element (RVE) or unit cell (UC) is the smallest volume over which a measurement can be ma... Read More about Representative Volume Elements and Unit Cells: Concepts, Theory, Applications and Implementation.

The Maximum Stress Failure Criterion and the Maximum Strain Failure Criterion: Their Unification and Rationalization (2020)
Journal Article
Li, S. (2020). The Maximum Stress Failure Criterion and the Maximum Strain Failure Criterion: Their Unification and Rationalization. Journal of Composites Science, 4(4), Article 157. https://doi.org/10.3390/jcs4040157

The maximum strain failure criterion is unified with the maximum stress failure criterion, after exploring the implications of two considerations responsible for this: (1) the failure strains for the direct strain components employed in the maximum s... Read More about The Maximum Stress Failure Criterion and the Maximum Strain Failure Criterion: Their Unification and Rationalization.

A reflection on the Mohr failure criterion (2020)
Journal Article
Li, S. (2020). A reflection on the Mohr failure criterion. Mechanics of Materials, 148, Article 103442. https://doi.org/10.1016/j.mechmat.2020.103442

The Mohr failure criterion has been reexamined and represented in a rational manner in the context of brittle materials. The generic assumptions and their logical inferences have been elaborated, as well as the basic assumption of the isotropy of the... Read More about A reflection on the Mohr failure criterion.

Unification and parameterisation of 2D and 3D weaves and the formulation of a unit cell for composites made of such preforms (2020)
Journal Article
Xu, M., Sitnikova, E., & Li, S. (2020). Unification and parameterisation of 2D and 3D weaves and the formulation of a unit cell for composites made of such preforms. Composites Part A: Applied Science and Manufacturing, 133, Article 105868. https://doi.org/10.1016/j.compositesa.2020.105868

In this paper, the method to unify the definition of woven architectures in textile composites over a wide range of variations has been established. This was achieved via parametrisation of the weaves, which was conducted employing a limited set of c... Read More about Unification and parameterisation of 2D and 3D weaves and the formulation of a unit cell for composites made of such preforms.

Closed-Form Solution for Secondary Perturbation Displacement in Finite-Element-Implemented Koiter’s Theory (2020)
Journal Article
Yan, J., & Li, S. (2020). Closed-Form Solution for Secondary Perturbation Displacement in Finite-Element-Implemented Koiter’s Theory. AIAA Journal, 58(4), 1-12. https://doi.org/10.2514/1.j058941

The finite-element-implemented Koiter’s initial postbuckling analysis has not managed to convince commercial finite element code developers to incorporate it into their codes to benefit structural designers and analysts. Three key obstacles have been... Read More about Closed-Form Solution for Secondary Perturbation Displacement in Finite-Element-Implemented Koiter’s Theory.

On the Representativeness of the Cohesive Zone Model in the Simulation of the Delamination Problem (2019)
Journal Article
Sitnikova, E., Li, D., Wei, J., Yi, X., & Li, S. (2019). On the Representativeness of the Cohesive Zone Model in the Simulation of the Delamination Problem. Journal of Composites Science, 3(1), Article 22. https://doi.org/10.3390/jcs3010022

With the development of finite element (FE) codes, numerical modelling of delamination is often considered to be somewhat commonplace in modern engineering. However, the readily available modelling techniques often undermine the truthful understandin... Read More about On the Representativeness of the Cohesive Zone Model in the Simulation of the Delamination Problem.

Computational mechanical characterization of geometrically transformed Schwarz P lattice tissue scaffolds fabricated via two photon polymerization (2PP) (2018)
Journal Article
Zabidi, A. Z., Li, S., Felfel, R. M., Thomas, K. G., Grant, D. M., Mcnally, D., & Scotchford, C. (2019). Computational mechanical characterization of geometrically transformed Schwarz P lattice tissue scaffolds fabricated via two photon polymerization (2PP). Additive Manufacturing, 25, 399-411. https://doi.org/10.1016/j.addma.2018.11.021

Schwarz P unit cell-based tissue scaffolds comprised of poly(D,L-lactide-co-caprolactone)(PLCL) fabricated via the additive manufacturing technique, two-photon polymerisation (2PP) were found to undergo geometrical transformations from the original i... Read More about Computational mechanical characterization of geometrically transformed Schwarz P lattice tissue scaffolds fabricated via two photon polymerization (2PP).

Damage related material constants in continuum damage mechanics for unidirectional composites with matrix cracks (2018)
Journal Article
Li, S., Wang, M., Jeanmeure, L., Sitnikova, E., Yu, F., Pan, Q., …Talreja, R. (2019). Damage related material constants in continuum damage mechanics for unidirectional composites with matrix cracks. International Journal of Damage Mechanics, 28(5), 690-707. https://doi.org/10.1177/1056789518783239

Application of a continuum damage mechanics formulation rests on the ease with which the material constants involved in the formulation can be determined. For an initially linear elastic material, the changes in elastic constants induced by damage de... Read More about Damage related material constants in continuum damage mechanics for unidirectional composites with matrix cracks.

The unit cell method in predictions of thermal expansion properties of textile reinforced composites (2018)
Journal Article
Gou, J.-J., Gong, C.-L., Gu, L.-X., Li, S., & Tao, W.-Q. (2018). The unit cell method in predictions of thermal expansion properties of textile reinforced composites. Composite Structures, 195, 99-117. https://doi.org/10.1016/j.compstruct.2018.04.045

Thermal expansion properties of textile reinforced composites with certain structure symmetries can be efficiently calculated by a size-limited unit cell. In this paper, a general approach is developed for the establishment of such a unit cell model.... Read More about The unit cell method in predictions of thermal expansion properties of textile reinforced composites.

A critical review on the rationality of popular failure criteria for composites (2018)
Journal Article
Li, S., & Sitnikova, E. (2018). A critical review on the rationality of popular failure criteria for composites. https://doi.org/10.1016/j.coco.2018.02.002

Popular failure criteria for fibre reinforced composites are subjected to critical scrutiny on their rationality. The rationality of a theory is about the mathematical and physical logic underlying the theory, rather than the closeness of their resul... Read More about A critical review on the rationality of popular failure criteria for composites.

An excursion into representative volume elements and unit cells (2017)
Book Chapter
Li, S., & Sitnikova, E. (2017). An excursion into representative volume elements and unit cells. In P. W. Beaumont, & C. H. Zweben (Eds.), Comprehensive Composite Materials II, Volume 1, Reinforcements and General Theories of Composites (451-489). Amsterdam: Elsevier. https://doi.org/10.1016/B978-0-12-803581-8.10352-2

The objective of this chapter is to provide a comprehensive and systematic account on the subject of representative volume elements (RVEs) and unit cells (UCs). To construct an RVE or UC, intuition has been often perceived sufficient to facilitate th... Read More about An excursion into representative volume elements and unit cells.

The Tsai-Wu failure criterion rationalised in the context of UD composites (2017)
Journal Article
Li, S., Sitnikova, E., Liang, Y., & Kaddour, A. S. (2017). The Tsai-Wu failure criterion rationalised in the context of UD composites. Composites Part A: Applied Science and Manufacturing, 102, 207-217. https://doi.org/10.1016/j.compositesa.2017.08.007

© 2017 The Authors This paper is to rationalise the empirical aspect of the Tsai-Wu failure criterion in the context of UD composites associated with the determination of the interactive strength property F12 based on the analytic geometry. It reveal... Read More about The Tsai-Wu failure criterion rationalised in the context of UD composites.

Subtle features of delamination in cross-ply laminates due to low speed impact (2017)
Journal Article
Sitnikova, E., Li, S., Li, D., & Yi, X. (2017). Subtle features of delamination in cross-ply laminates due to low speed impact. Composites Science and Technology, 149, 149-158. https://doi.org/10.1016/j.compscitech.2017.06.021

In cross-ply laminates, the shape of delamination areas, which form due to low velocity impact, have two subtle features, which have been observed consistently in numerous experiments. Those are the pointed delamination tips and the intact zone betwe... Read More about Subtle features of delamination in cross-ply laminates due to low speed impact.

On understanding the applicability of Mohr-Coulomb failure hypothesis for composite materials using UnitCells© (2016)
Presentation / Conference Contribution
Balasubramani, N. K., Sitnikova, E., & Li, S. (2016). On understanding the applicability of Mohr-Coulomb failure hypothesis for composite materials using UnitCells©.

The applicability of Mohr-Coulomb (M-C) failure hypothesis for anisotropic composite materials is re-examined in this paper. Mohr-Coulomb failure theory has been widely referred to in the literature to study the failure of unidirectional (UD) fibre r... Read More about On understanding the applicability of Mohr-Coulomb failure hypothesis for composite materials using UnitCells©.

The flexural properties of composite repaired pipeline: Numerical simulation and experimental validation (2015)
Journal Article

Finite element analysis (FEA) modelling of fiber-reinforced polymer (FRP) repair in offshore risers (2015)
Book Chapter
Johnson, M., Chan, P., Tshai, K., & Li, S. (2015). Finite element analysis (FEA) modelling of fiber-reinforced polymer (FRP) repair in offshore risers. Rehabilitation of pipelines using fibre reinforced polymer (FRP) composites (177-210). Woodhead Publishing. https://doi.org/10.1016/B978-0-85709-684-5.00009-6

The use of relatively inexpensive, high strength to weight ratio fiber reinforced polymer composite (FRPC) as a load bearing pipe repair sleeve is an emerging technology that is becoming common for offshore applications. This chapter will first outli... Read More about Finite element analysis (FEA) modelling of fiber-reinforced polymer (FRP) repair in offshore risers.

A composite material characterisation tool: UnitCells (2015)
Journal Article
Li, S., Jeanmeure, L. F. C., & Pan, Q. (2015). A composite material characterisation tool: UnitCells. Journal of Engineering Mathematics, 95, 279-293. https://doi.org/10.1007/s10665-014-9776-4

Unit cells in conjunction with micromechanical finite-element analysis have been widely used as a means for material characterisation of modern composites. However, they have been mostly applied in an ad hoc manner based on individual cases. Their im... Read More about A composite material characterisation tool: UnitCells.

Reflection on 'finite rotation problem' in plate and shell theories and in finite element formulation - Back to basics (2014)
Journal Article
Li, S. (2015). Reflection on 'finite rotation problem' in plate and shell theories and in finite element formulation - Back to basics. International Journal of Mechanical Sciences, 91, 12-17. https://doi.org/10.1016/j.ijmecsci.2014.07.004

This paper results from a reflection on the problem of finite rotations in plates and shells and its presentation in finite element formulation, a well-attended subject with a wide diversity of treatments, often extremely complicated. For instance, t... Read More about Reflection on 'finite rotation problem' in plate and shell theories and in finite element formulation - Back to basics.

Burst strength of carbon fibre reinforced HDPE strip pipeline repair system: a numerical and experimental approach (2014)
Journal Article

Oil and gas pipelines are susceptible to various forms of damage where repair mechanisms have since been developed for rehabilitation. Once installed, structural health monitoring often incurs excessive costs and defects rectification of the repaired... Read More about Burst strength of carbon fibre reinforced HDPE strip pipeline repair system: a numerical and experimental approach.

Boundary conditions resulting from cylindrical and longitudinal periodicities (2013)
Journal Article
Kyaw, S., Li, S., & Jones, A. (2014). Boundary conditions resulting from cylindrical and longitudinal periodicities. Computers and Structures, 133, 122-130. https://doi.org/10.1016/j.compstruc.2013.11.017