Efficient strong Unified Formulation for stress analysis of non-prismatic beam structures

Ojo, Saheed Olalekan

doi:10.1016/j.compstruct.2021.114190

Cited by 9 publications

(4 citation statements)

References 37 publications

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“…where 𝐹 𝜏 is the function that captures the cross-sectional deformation and can be expanded to any order 𝜏 for the enrichment of the beam's kinematical description. The cross-sectional function 𝐹 𝜏 adopted in this study is the so-called Serendipity Lagrange expansion (SLE) function that describes the cross-sectional behaviour of the beam accurately and efficiently without the need for re-meshing or loss of numerical stability (for example, see [21][22][23][24]). The stresses (𝝈 = [ 𝜎 𝑥𝑥 𝜎 𝑦𝑦 𝜎 𝑧𝑧 𝜏 𝑦𝑧 𝜏 𝑥𝑧 𝜏 𝑥𝑦] 𝑇 ) and strains (𝜺 = [ 𝜀 𝑥𝑥 𝜀 𝑦𝑦 𝜀 𝑧𝑧 𝛾 𝑦𝑧 𝛾 𝑥𝑧 𝛾 𝑥𝑦] 𝑇 ) relationship is governed by…”

Section: Unified Formulation Preliminariesmentioning

confidence: 99%

“…According to many studies, UF-based models have proved effective for accurate prediction of static, buckling, dynamic and free vibration, and postbuckling responses [16][17][18][19]. As a further development to achieve spectral convergence, the theory of UF has been explored within the context of strong form systems combined with high-order numerical methods like the differential quadrature method (DQM) and radial basis function to realise efficient predictions of linear static [20][21][22][23], dynamic [20], buckling [20] and large deflection [24][25][26] responses of constant stiffness and variable stiffness composite structures. In another development, UF-based strong form systems combined with the recently proposed inverse differential quadrature method (iDQM) [27][28] have shown promise of spectral convergence for linear static analysis of composite beams [29].…”

Section: Introductionmentioning

confidence: 99%

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Free Vibration Analysis of Thermally Prestressed Constant and Variable Stiffness Laminated Beams using Strong Unified Formulation

Ojo,

Zucco,

Weaver

2023

9th ECCOMAS Thematic Conference on the Mechanical Response of Composites

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Free vibration analysis is an essential requirement to capture the behaviour of composite structures subject to dynamic loading environment. To enhance the vibratory behaviour of composite structures, variable stiffness (VS) concept offers increased design flexibilities to tailor the structural response to meet a wide range of applications. Mechanically, the increased design space created by VS techniques leads to complexities of non-classical stiffness couplings which necessitate robust computational frameworks with enriched kinematics to predict the dynamic response accurately and efficiently. In this regard, this study proposes an enhanced differential quadrature based Strong Unified Formulation (SUF) to investigate the free vibration behaviour of thermally prestressed constant and variable stiffness composite beams. The proposed SUF model exploits the flexible kinematical description of the Theory of Unified Formulation to combine a hierarchical serendipity Lagrange-based 2D finite element (FE) with 1D differential quadrature method beam element for efficient free vibration characterisation of composite beams induced with prestress at different temperatures. The proposed SUF free vibration solutions of constant stiffness and VS beams demonstrate satisfactory accuracy and achieved improved efficiency with up to 99.9% computational savings when benchmarked against ABAQUS 3D FE solutions. Finally, a numerical study reveals that the effects of thermal prestress significantly contribute to the free vibration response of constant stiffness and VS laminated beams underscoring the importance of the study.

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Section: Unified Formulation Preliminariesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Free Vibration Analysis of Thermally Prestressed Constant and Variable Stiffness Laminated Beams using Strong Unified Formulation

Ojo,

Zucco,

Weaver

2023

9th ECCOMAS Thematic Conference on the Mechanical Response of Composites

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“…The results indicated that the accuracy of the calculation of stress was more while applying inverse DQM. Ojo et al 35 investigated a 3D stress analysis of VSCL beams undergoing large deflections using a strong unified formulation. It was shown that VSCL beams with the same structural configuration exhibited different behaviour under different loading conditions due to the tailored structural properties.…”

Section: Introductionmentioning

confidence: 99%

Post-buckling of variable stiffness curvilinear fibre-reinforced general lay-up composite beams by sinusoidal shear flexible theory

Ganapathi

Polit

Haboussi

et al. 2023

Journal of Reinforced Plastics and Composites

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The mechanical post-buckling behaviour of variable stiffness layered composite beams reinforced by curvilinear fibres subjected to compressive loads is investigated here using a sine function-based shear flexible beam model. The neutral axis stretching force stemming from the axial movement restraints is accounted for through von Karman’s assumption based geometrical nonlinearity. Furthermore, the modified beam constitutive equation arising from the consideration of the Poisson’s effect is introduced in the formulation for the laminated beam analysis with general lay-up or ply sequences. The governing equations incorporating the incremental stiffness matrices are formed through the minimization of total potential energy principle and are solved by numerical method. The solutions for the developed governing equations are evaluated iteratively based on eigenvalue analysis and the characteristics of post-buckling of laminated beams can be inferred through the relationship between the beam deflection level and post-buckling axial load. An in-depth analysis selecting many design parameters for instance lamina’s curvilinear fibre angles, beam slenderness ratio, lay-up and edge conditions, load type and so on is dealt with in bringing out the behaviour of variable stiffness laminated beam in linear and post-buckling regions. Also, the influence of flexible end supports by restraining elastically against ends rotation is studied on the beam elastic stability behaviour.

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“…According to the deformation performance, the lattice materials can be divided into stretchingdominated and bending-dominated structures, and the stretch-dominated structures exhibit superior stiffness and strength than the bending-dominated ones. [4] Until now, a lot of lattice structure topologies have been found such as pyramidal lattice, [5][6][7] kagome lattice structure, [8] octet lattice material, [9] tetrahedral lattice, [10] corrugated structure, [11] prismatic structure, [12] and hourglass lattice. [13] Previous investigations on the mechanical behavior of various lattice materials are mostly focused on predicting the macroscopic stiffness and strength experimentally, numerically and theoretically.…”

Section: Introductionmentioning

confidence: 99%

Experimental and Simulation Analysis on the Mechanical Behavior of 3D‐Enhanced Al‐Based Tetrahedral Lattice Materials

Xue

Huang

et al. 2022

Physica Status Solidi (a)

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Herein, the compressive mechanical behavior of novel 3D tetrahedral lattice materials is investigated by ways of experimental, numerical, and analytical methods with a good performance of accuracy. Samples with varied length–diameter ratios are fabricated through 3D printing combined with investment casting method. The compressive behavior, deformation characteristic, and energy property of the lattice materials are comprehensively recorded and analyzed with respect to the geometric parameter and compression directions. It is observed that the length–diameter ratio exhibits a significant influence on the mechanical performance and energy absorption of the materials, that is, the lower the length–diameter ratio, the higher the relative density, strength, and energy absorption. Good agreements are observed among the experimental, numerical, and analytical results within a relative acceptable error. Moreover, the mechanical properties and deformation characteristics of lattice materials depend on compression directions to a great extent. In addition, the novel tetrahedral lattice materials with reasonable relative density present superior performance features compared with the other cellular materials.

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Efficient strong Unified Formulation for stress analysis of non-prismatic beam structures

Cited by 9 publications

References 37 publications

Free Vibration Analysis of Thermally Prestressed Constant and Variable Stiffness Laminated Beams using Strong Unified Formulation

Free Vibration Analysis of Thermally Prestressed Constant and Variable Stiffness Laminated Beams using Strong Unified Formulation

Post-buckling of variable stiffness curvilinear fibre-reinforced general lay-up composite beams by sinusoidal shear flexible theory

Experimental and Simulation Analysis on the Mechanical Behavior of 3D‐Enhanced Al‐Based Tetrahedral Lattice Materials

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