Design of tension structures and shells using the Airy stress function

Discontinuities in the Airy stress function for in-plane stress analysis represent forces and moments in connected one-dimensional elements. We expand this representation to curved membrane-action structures, such as shells and cable nets, and graphically visualise the internal stresses and section forces at the boundary necessary for equilibrium. The approach enhances understanding of the interplay between form and forces and can support design decisions related to form-finding and force efficiency. As illustrative examples, the prestressing needed for three existing cable nets is determined, and its influence on the edge-beam bending moment is explored.

The thiol-disulfide exchange activity of AtPDI1 is involved in the response to abiotic stresses

Background Arabidopsis protein disulfide isomerase 1 (AtPDI1) has been demonstrated to have disulfide isomerase activity and to be involved in the stress response. However, whether the anti-stress function is directly related to the activities of thiol-disulfide exchange remains to be elucidated. Results In the present study, encoding sequences of AtPDI1 of wild-type (WT) and double-cysteine-mutants were transformed into an AtPDI1 knockdown Arabidopsis line (pdi), and homozygous transgenic plants named pdi-AtPDI1, pdi-AtPDI1m1 and pdi-AtPDI1m2 were obtained. Compared with the WT and pdi-AtPDI1, the respective germination ratios of pdi-AtPDI1m1 and pdi-AtPDI1m2 were significantly lower under abiotic stresses and exogenous ABA treatment, whereas the highest germination rate was obtained with AtPDI1 overexpression in the WT (WT- AtPDI1). The root length among different lines was consistent with the germination rate; a higher germination rate was observed with a longer root length. When seedlings were treated with salt, drought, cold and high temperature stresses, pdi-AtPDI1m1, pdi-AtPDI1m2 and pdi displayed lower survival rates than WT and AtPDI1 overexpression plants. The transcriptional levels of ABA-responsive genes and genes encoding ROS-quenching enzymes were lower in pdi-AtPDI1m1 and pdi-AtPDI1m2 than in pdi-AtPDI1. Conclusion Taken together, these results clearly suggest that the anti-stress function of AtPDI1 is directly related to the activity of disulfide isomerase.

Analysis of Beam Bending with an Elliptical Cross-Section

This paper calculates the stress function constants to determine and analyse the stress field of a beam with an elliptical cross-section under transverse loading. This was performed using linear elasticity principles. The Beltrami-Michell compatibility equations were used to derive the formulas used to calculate these parameters in the beam with the elliptical cross-section. This paper uses dimensionless analysis to comprehend the effect of each variable in the problem. The loading was applied at the centre of the right-end face of the elliptical beam. This loading configuration is the same as an existing linear elasticity problem; however, that problem models a cylindrical beam instead of an elliptical one. Thus, the existing parameters from the cylindrical model were used to verify the formulas, calculated in this paper, for the elliptical beam.

Modelling of Elongational Flow of HDPE Melts by Hierarchical Multi-Mode Molecular Stress Function Model

The transient elongational data set obtained by filament-stretching rheometry of four commercial high-density polyethylene (HDPE) melts with different molecular characteristics was reported by Morelly and Alvarez [Rheologica Acta 59, 797–807 (2020)]. We use the Hierarchical Multi-mode Molecular Stress Function (HMMSF) model of Narimissa and Wagner [Rheol. Acta 54, 779–791 (2015), and J. Rheology 60, 625–636 (2016)] for linear and long-chain branched (LCB) polymer melts to analyze the extensional rheological behavior of the four HDPEs with different polydispersity and long-chain branching content. Model predictions based solely on the linear-viscoelastic spectrum and a single nonlinear parameter, the dilution modulus GD for extensional flows reveals good agreement with elongational stress growth data. The relationship of dilution modulus GD to molecular characteristics (e.g., polydispersity index (PDI), long-chain branching index (LCBI), disengagement time τd) of the high-density polyethylene melts are presented in this paper. A new measure of the maximum strain hardening factor (MSHF) is proposed, which allows separation of the effects of orientation and chain stretching.

Displacements and Stress Functions of Straight Dislocations and Line Forces in Anisotropic Elasticity: A New Derivation and Its Relation to the Integral Formalism

The displacement and stress function fields of straight dislocations and lines forces are derived based on three-dimensional anisotropic incompatible elasticity. Using the two-dimensional anisotropic Green tensor of generalized plane strain, a Burgers-like formula for straight dislocations and body forces is derived and its relation to the solution of the displacement and stress function fields in the integral formalism is given. Moreover, the stress functions of a point force are calculated and the relation to the potential of a Dirac string is pointed out.

Minimizing the Negative Effects of Coolant Channels on the Torsional and Torsional-Axial Stiffness of Drills

Coolant channels allow internal coolant delivery to the cutting region and significantly improve drilling, but these channels also reduce the torsional and torsional-axial stiffness of the drills. Such a reduction in stiffness can degrade the quality of the drilled holes. The evacuation of cutting chips and the delivery of the cutting fluid put strict geometrical restrictions on the cross-section design of the drill. This necessitates careful selection and optimization of features such as the geometry of the coolant channels. This paper presents a new method that uses Prandtl’s stress function to predict the torsional and torsional-axial stiffness values. Using this method drills with one central channel are compared to those with two eccentric coolant channels, which shows that with the same cross-section area, the reduction of axial and torsional-axial stiffness is notably smaller for the design with two eccentric channels compared to a single central channel. The stress function method is further used to select the appropriate location of the eccentric coolant channels to minimize the loss of torsional and torsional-axial stiffness. These results are verified by comparison to the results of three-dimensional finite element analyses.

Stress-Function Variational Method for Accurate Free-Edge Interfacial Stress Analysis of Adhesively Bonded Single-Lap Joints and Single-Sided Joints

Large free-edge interfacial stresses induced in adhesively bonded joints (ABJs) are responsible for the commonly observed debonding failure in ABJs. Accurate and efficient stress analysis of ABJs is important to the design, structural optimization, and failure analysis of ABJs subjected to external mechanical and thermomechanical loads. This paper generalizes the high-efficiency semi-analytic stress-function variational methods developed by the authors for accurate free-edge interfacial stress analysis of ABJs of various geometrical configurations. Numerical results of the interfacial stresses of two types of common ABJs, i.e., adhesively bonded single-lap joints and adhesively single-sided joints, are demonstrated by using the present method, which are further validated by finite element analysis (FEA). The numerical procedure formulated in this study indicates that the present semi-analytic stress-function variational method can be conveniently implemented for accurate free-edge interfacial stress analysis of various type of ABJs by only slightly modifying the force boundary conditions. This method is applicable for strength analysis and structural design of broad ABJs made of multi-materials such as composite laminates, smart materials, etc.

Fourier Integral Transformation Method for Solving Two Dimensional Elasticity Problems in Plane Strain Using Love Stress Functions

The Fourier integral method was used in this work to determine the stress fields in a two dimensional (2D) elastic soil mass of semi-infinite extent subject to line and strip loads of uniform intensity acting on the boundary. The two dimensional plane strain problem was formulated using stress-based method. The Fourier integral was used to transform the biharmonic stress compatibility equation to a fourth order linear ordinary differential equation (ODE) in terms of the stress function. The ODE was solved subject to the boundedness condition to obtain the bounded stress function. Cartesian stress components were obtained using the Love stress functions. Application of the stress boundary conditions for the case of line load of uniform intensity and the cases of uniformly distributed load on a strip of finite width gave the respective unknown constants of the Love stress functions; and hence the complete determination of the Cartesian stress components for the two cases considered. Inversion of the Fourier integral expressions obtained for the normal and shear stresses in the Fourier parameter gave respective expressions for the normal and shear stress fields for line and finite strip loads of finite width in the physical domain variables. The results obtained agreed with the results from previous studies which used displacement based methods.