Towards a universal shear correction factor in filament stretching rheometry

Filament stretching rheometry is a prominent experimental method to determine rheological properties in extensional flow whereby the separating plates determine the extension rate. In literature, several correction factors that can compensate for the errors introduced by the shear contribution near the plates have been introduced and validated in the linear viscoelastic regime. In this work, a systematic analysis is conducted to determine if a material-independent correction factor can be found for non-linear viscoelastic polymers. To this end, a finite element model is presented to describe the flow and resulting stresses in the filament stretching rheometer. The model incorporates non-linear viscoelasticity and a radius-based controller for the plate speed is added to mimic the typical extensional flow in filament stretching rheometry. The model is validated by comparing force simulations with analytical solutions. The effects of the end-plates on the extensional flow and resulting force measurements are investigated, and a modification of the shear correction factor is proposed for the non-linear viscoelastic flow regime. This shows good agreement with simulations performed at multiple initial aspect ratios and strain rates and is shown to be valid for a range of polymers with non-linear rheological behaviour.

Mindlin-Reissner Analytical Model with Curvature for Tunnel Ventilation Shafts Analysis

The formulation and analytic solution of a new mathematical model with constitutive curvature for analysis of tunnel ventilation shaft wall is proposed. Based on the Mindlin–Reissner theory for thick shells, this model also takes into account the shell constitutive curvature and considers an expression of the shear correction factor variable (αn) in terms of the thickness (h) and the radius of curvature (R). The main advantage of the proposed model is that it has the possibility to analyze thin, medium and thick tunnel ventilation shafts. As a result, two comparisons were made: the first one, between the new model and the Mindlin–Reissner model without constitutive curvature with the shear correction factor αn=5/6 as a constant, and the other, between the new model and the tridimensional numerical models (solids and shells) obtained by finite element method for different slenderness ratios (h/R). The limitation of the proposed model is that it is to be formulated for a general linear-elastic and axial-symmetrical state with continuous distribution of the mass.

Mindlin-Reissner Analytical Model with Curvature for Tunnel Ventilation Shafts Analysis

The formulation and analytic solution of a new mathematical model with constitutive curvature for analysis of tunnel ventilation shaft wall is proposed. Based on the Mindlin-Reissner theory for thick shells, this model also takes into account the shell constitutive curvature and considers an expression of the shear correction factor variable (αn) in terms of the thickness (h) and the radius of curvature (R). The main advantage of the proposed model is that it has the possibility to analyze thin, medium and thick tunnel ventilation shafts. As a result, two comparisons were made: the first one, between the new model and the Mindlin-Reissner model without constitutive curvature with the shear correction factor (α_n=6/5) as a constant, and the other, between the new model and the tridimensional numerical models (solids and shells) obtained by finite element method for different slenderness ratios (h/R). The limitation of the proposed model is that it is to be formulated for a general linear-elastic and axial-symmetrical state with continuous distribution of the mass.

Porous Functionally Graded Plates: An Assessment of the Influence of Shear Correction Factor on Static Behavior

The known multifunctional characteristic of porous graded materials makes them very attractive in a number of diversified application fields, which simultaneously poses the need to deepen research efforts in this broad field. The study of functionally graded porous materials is a research topic of interest, particularly concerning the modeling of porosity distributions and the corresponding estimations of their material properties—in both real situations and from a material modeling perspective. This work aims to assess the influence of different porosity distribution approaches on the shear correction factor, used in the context of the first-order shear deformation theory, which in turn may introduce significant effects in a structure’s behavior. To this purpose, we evaluated porous functionally graded plates with varying composition through their thickness. The bending behavior of these plates was studied using the finite element method with two quadrilateral plate element models. Verification studies were performed to assess the representativeness of the developed and implemented models, namely, considering an alternative higher-order model also employed for this specific purpose. Comparative analyses were developed to assess how porosity distributions influence the shear correction factor, and ultimately the static behavior, of the plates.

Static analyses of laminated rhombic conoids

Purpose This paper aims to present a new mathematical model for laminated rhombic conoids with reasonable thickness and depth. The presented model does not require the shear correction factor, as transverse strain variation through the thickness was assumed as a parabolic function. The zero transverse shear stress provision at the bottom and the top of rhombic conoids was enforced in the model. The presented model implemented a C0 finite element (FE) model, eliminating C1 continuity requirement in the mathematical model. The proposed model was validated with analytical, experimental and other methods derived from the literature. Design/methodology/approach A novel mathematical model for laminated composite skew conoidal shells has been proposed. Parabolic transverse shear strain deformation across thickness is considered. FE coding of the proposed novel mathematical model was done. Slope continuity requirement associated with present FE coding has been suitably avoided. No shear correction factor is required in the present formulation. Findings This is the first attempt to study the bending response of laminated rhombic conoids with reasonable thickness and depth. After comparisons, the parametric study was performed by varying the skew angles, boundary conditions, thickness ratios and the minimum rise to maximum rise (hl/hh) ratio. Originality/value The novelty of the presented model is reflected by the simultaneous addition of twist curvature in the strain field as well as the curvature in the displacement field allowing the accurate analysis of reasonably thick and deep laminated composite rhombic conoids. The behavior of conoids differs from that of usual shells such as cylindrical and spherical due to the conoid’s inherent twist curvature with its complex geometry and different location of maximum deflection.

Studies Regarding the Shear Correction Factor in the Mindlin Plate Theory for Sandwich Plates

The displacement field from the first-order shear deformation plate theory (FSDT) extents the cinematic aspect of the classical theory of laminated plates (CLPT), including a transverse shear deformation, considered constant on the plate thickness. In order to correct this aspect, in FSDT (named also the Mindlin plate theory) a coefficient Ks was inserted, named shear correction factor, used as a multiplier in the shear stiffness equation of the plate. In this paper are presented the most popular methods for determination of the shear correction factor, identifying the differences between them. To emphasize the influence of the shear correction factor on the stress response, a numerical parametric study was done on some sandwich plates filled with polyurethane foam. The processing of the obtained results allow drawing some conclusions useful in the designing of this type of sandwich plates.