Title: Post-Buckling Mechanics of a Square Slender Steel Plate in Pure Shear
Thin (slender) steel plates possess shear strength beyond the elastic buckling load which is commonly referred to as the post-buckling capacity. Semi-empirical equations based on experimental tests of plate girders have been used for decades to predict the ultimate post-buckling strength of slender webs. However, several recent studies have shown that the current models for predicting the ultimate shear post-buckling capacity of thin plates are based on some incorrect assumptions regarding their mechanical behavior. As a result, the current design equations provide an approximate estimate of capacity for the range of parameters in the test data upon which they are founded. This paper explores the fundamental behavior of thin plates under pure shear. Such a fundamental examination of shear post-buckling behavior in thin plates is needed to enable design procedures that can optimize a plate’s shear strength and load-deformation performance for a wider range of loading and design parameters. Using finite element analyses, which are validated against available results of previous experimental tests, outputs such as plastic strains, von Mises stresses, principal stresses, and principal stress directions are examined on a buckled plate acting in pure shear. The internal bending, shear, and membrane stresses in the plate’s finite elements are also evaluated. In this study, these evaluations are performed for a simply-supported plate with an aspect ratio equal to 1.0 and slenderness ratio equal to 134. Results show that localized bending in the plates due to the out-of-plane post-buckling deformations appear to be a significant factor in the ultimate shear post-buckling capacity of the plate. Also, the compressive stresses continue to increase beyond the onset of elastic buckling in some regions of the plate, contrary to current design assumptions. Overall, this study provides new insights into the mechanics of shear post-buckling behavior of thin plates that can be exploited for design procedures that are consistent with mechanical behavior. more »« less
Childs, Jake A.; Rucker, Caleb
(, Frontiers in Robotics and AI)
null
(Ed.)
Developing high-strength continuum robots can be challenging without compromising on the overall size of the robot, the complexity of design and the range of motion. In this work, we explore how the load capacity of continuum robots can drastically be improved through a combination of backbone design and convergent actuation path routing. We propose a rhombus-patterned backbone structure composed of thin walled-plates that can be easily fabricated via 3D printing and exhibits high shear and torsional stiffness while allowing bending. We then explore the effect of combined parallel and converging actuation path routing and its influence on continuum robot strength. Experimentally determined compliance matrices are generated for straight, translation and bending configurations for analysis and discussion. A robotic actuation platform is constructed to demonstrate the applicability of these design choices.
We develop a method for estimation of parameters of an elastic plate resting on a Winkler-type elastic foundation solely from data on the vertical displacements of the plate. The method allows one to estimate components of the external body force density field, plate thickness, elastic foundation stiffness parameters, horizontal displacements of the plate, and stresses. The key idea of the method is that multiple plate models are used simultaneously, namely the proposed reduced three-dimensional (R3D) plate model, the Mindlin plate model, and the thin plate model. The three plate models form a hierarchy of elastic plate models based on assumptions imposed on stresses, with the R3D plate model being the most generalized model and the thin plate model being the most constrained one. The hierarchical relationship among the plate models allows one to incorporate prior information into the estimation technique. The applicability of the proposed estimation method is illustrated by a numerical example.
Abstract Mechanical metamaterials with negative Poisson’s ratio (NPR) have emerged as a novel class of engineering material, and have attracted increasing attention in various engineering sectors. Most studies available on the buckling problem of laminated plates with positive or NPR are those under uniaxial compression. Here, we report that the buckling phenomenon may occur for auxetic nanocomposite laminated plates under uniaxial tension when the unloaded edges of the plates are immovable. Two types of nanocomposites are considered, including graphene/Cu and carbon nanotube/Cu composites. Governing equations of the auxetic nanocomposite laminated plates are formulated based on the framework of Reddy’s higher-order shear deformation theory. In modeling, the von Kármán nonlinear strain–displacement relationship, temperature-dependent material properties, thermal effects, and the plate–substrate interaction are considered. The explicit analytical solutions for postbuckling of auxetic nanocomposite laminated plates subjected to uniaxial tension are obtained for the first time by employing a two-step perturbation approach. Numerical investigations are performed for tension buckling and postbuckling behaviors of auxetic nanocomposite laminated rectangular plates with in-plane NPR rested on an elastic substrate under temperature environments.
Yost, Joseph Robert; Akbarzadeh, Masoud; Bolhassani, Mohammad; Ryan, Liam; Schneider, Jens; Chhadeh, Philipp Amir
(, International Conference on Civil Engineering and Architectural Design)
null
(Ed.)
This research presents an experimental program executed to understand the strength and stiffness properties of hollow built-up glass compression members that are intended for use in the modular construction of all glass, compression-dominant, shell-type structures. The proposed compression-dominant geometric form has been developed using the methods of form finding and three-dimensional graphical statics. This research takes the first steps towards a new construction methodology for glass structures where individual hollow glass units (HGU) are assembled using an interlocking system to form large, compression-dominant, shell-type structures, thereby exploiting the high compression strength of glass. In this study, an individual HGU has an elongated hexagonal prism shape and consists of two deck plates, two long side plates, and four short side plates, as is shown in Figure 1. Connections between glass plates are made using a two-sided transparent structural adhesive tape. The test matrix includes four HGUs, two each fabricated with 1 mm and 2 mm thick adhesive tape. All samples are dimensioned 64 cm on the long axis of symmetry, 51 cm on the short axis of symmetry, and are 10 cm in width. Glass plates are all 10 mm thick annealed float glass with geometric fabrication done using 5-axis abrasive water jet cutting. HGU assembly is accomplished using 3D printed truing clips and results in a rigid three-dimensional glass frame. Testing was done with the HGU oriented such that load was introduced on the short side edges of the two deck plates, resulting in an asymmetric load-support condition. A soft interface material was used between the HGU and steel plates of the hydraulic actuator and support for the purpose of avoiding premature cracking from local stress concentrations on the glass edges at the load and support locations. Force was applied in displacement control at 0.25 mm/minute with a full array of displacement and strain sensors. Test results for load vs. center deck plate transverse deflection are shown in Figure 2. All samples failed explosively by flexural buckling with no premature cracking on the load and support edges of the deck plates. Strain and deformation data clearly show the presence of second-order behavior resulting from bending deformation perpendicular to the plane of the deck plates. In general, linear axial behavior transitions to nonlinear second-order behavior, with increasing rates in deflection and strain growth, ultimately ending in glass fracture on the tension surfaces of the buckled deck plates. The failure resulted in near-complete disintegration of the deck plates, but with no observable cracking in any side plates and a secure connection on all adhesive tape. Results of the experimental program clearly demonstrate the feasibility of using HGUs for modular construction of compression dominant all-glass shell-type structures. This method of construction can significantly reduce the self-weight of the structure, and it will inspire the use of sustainable materials in the construction of efficient structures.
Nally, A; Hambleton, James P
(, Proceedings of the 44th Annual Conference on Deep Foundations)
This work focuses on the numerical simulation of multi-plate anchor systems (e.g., helical anchors) in sand subjected to vertical loading. In assessing the stiffness and capacity of these multi-plate anchor systems, full awareness of the abilities and limitations of the various analysis methods must be understood. This work first summarizes studies completed by others and then goes on to assess the failure mechanisms of multi-plate anchors in sand and the influence of (1) plate width-to-depth ratio, (2) number of plates, and (3) relative positioning of plates. The analysis makes use of (1) conventional limit analysis, (2) so-called modified limit analysis that employs reduced strength parameters to account for the influence of soil dilatancy, and (3) the displacement-based finite element method, which considers elastic as well as plastic deformation leading to failure. The work critically reflects on limitations in the current analysis methods for helical ground anchors.
Garlock, M, Quiel, S, Wang, P, Alos-Moya, J, and Glassman, J. Post-Buckling Mechanics of a Square Slender Steel Plate in Pure Shear. Retrieved from https://par.nsf.gov/biblio/10098556. Engineering journal 56.1
Garlock, M, Quiel, S, Wang, P, Alos-Moya, J, & Glassman, J. Post-Buckling Mechanics of a Square Slender Steel Plate in Pure Shear. Engineering journal, 56 (1). Retrieved from https://par.nsf.gov/biblio/10098556.
Garlock, M, Quiel, S, Wang, P, Alos-Moya, J, and Glassman, J.
"Post-Buckling Mechanics of a Square Slender Steel Plate in Pure Shear". Engineering journal 56 (1). Country unknown/Code not available. https://par.nsf.gov/biblio/10098556.
@article{osti_10098556,
place = {Country unknown/Code not available},
title = {Post-Buckling Mechanics of a Square Slender Steel Plate in Pure Shear},
url = {https://par.nsf.gov/biblio/10098556},
abstractNote = {Thin (slender) steel plates possess shear strength beyond the elastic buckling load which is commonly referred to as the post-buckling capacity. Semi-empirical equations based on experimental tests of plate girders have been used for decades to predict the ultimate post-buckling strength of slender webs. However, several recent studies have shown that the current models for predicting the ultimate shear post-buckling capacity of thin plates are based on some incorrect assumptions regarding their mechanical behavior. As a result, the current design equations provide an approximate estimate of capacity for the range of parameters in the test data upon which they are founded. This paper explores the fundamental behavior of thin plates under pure shear. Such a fundamental examination of shear post-buckling behavior in thin plates is needed to enable design procedures that can optimize a plate’s shear strength and load-deformation performance for a wider range of loading and design parameters. Using finite element analyses, which are validated against available results of previous experimental tests, outputs such as plastic strains, von Mises stresses, principal stresses, and principal stress directions are examined on a buckled plate acting in pure shear. The internal bending, shear, and membrane stresses in the plate’s finite elements are also evaluated. In this study, these evaluations are performed for a simply-supported plate with an aspect ratio equal to 1.0 and slenderness ratio equal to 134. Results show that localized bending in the plates due to the out-of-plane post-buckling deformations appear to be a significant factor in the ultimate shear post-buckling capacity of the plate. Also, the compressive stresses continue to increase beyond the onset of elastic buckling in some regions of the plate, contrary to current design assumptions. Overall, this study provides new insights into the mechanics of shear post-buckling behavior of thin plates that can be exploited for design procedures that are consistent with mechanical behavior.},
journal = {Engineering journal},
volume = {56},
number = {1},
author = {Garlock, M and Quiel, S and Wang, P and Alos-Moya, J and Glassman, J.},
}
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