Nonlinear Mechanics of Interlocking Cantilevers

2017 ◽  
Vol 84 (12) ◽  
Author(s):  
Joseph J. Brown ◽  
Ryan C. Mettler ◽  
Omkar D. Supekar ◽  
Victor M. Bright
Keyword(s):  
Large Deflection ◽  
Elliptic Integral ◽  
Contact Point ◽  
Reaction Force ◽  
Insertion Force ◽  
Element Analysis ◽  
Fast Analysis ◽  
Analysis And Design ◽  
Physical Measurements ◽  
Compliant Systems

The use of large-deflection springs, tabs, and other compliant systems to provide integral attachment, joining, and retention is well established and may be found throughout nature and the designed world. Such systems present a challenge for mechanical analysis due to the interaction of contact mechanics with large-deflection analysis. Interlocking structures experience a variable reaction force that depends on the cantilever angle at the contact point. This paper develops the mathematical analysis of interlocking cantilevers and provides verification with finite element analysis and physical measurements. Motivated by new opportunities for nanoscale compliant systems based on ultrathin films and two-dimensional (2D) materials, we created a nondimensional analysis of retention tab systems. This analysis uses iterative and elliptic integral solutions to the moment–curvature elastica of a suspended cantilever and can be scaled to large-deflection cantilevers of any size for which continuum mechanics applies. We find that when a compliant structure is bent backward during loading, overlap increases with load, until a force maximum is reached. In a force-limited scenario, surpassing this maximum would result in snap-through motion. By using angled cantilever restraint systems, the magnitude of insertion force relative to retention force can vary by 50× or more. The mathematical theory developed in this paper provides a basis for fast analysis and design of compliant retention systems, and expands the application of elliptic integrals for nonlinear problems.

Parametric Deflection Approximations for End-Loaded, Large-Deflection Beams in Compliant Mechanisms

1995 ◽  
Vol 117 (1) ◽  
pp. 156-165 ◽  
Author(s):  
L. L. Howell ◽  
A. Midha
Keyword(s):  
Closed Form ◽  
Large Deflection ◽  
Numerical Solutions ◽  
Compliant Mechanisms ◽  
Elliptic Integral ◽  
Cantilever Beams ◽  
Simple Method ◽  
Body Angle ◽  
Analysis And Design ◽  
Integral Solutions

Geometric nonlinearities often complicate the analysis of systems containing large-deflection members. The time and resources required to develop closed-form or numerical solutions have inspired the development of a simple method of approximating the deflection path of end-loaded, large-deflection cantilever beams. The path coordinates are parameterized in a single parameter called the pseudo-rigid-body angle. The approximations are accurate to within 0.5 percent of the closed-form elliptic integral solutions. A physical model is associated with the method, and may be used to simplify complex problems. The method proves to be particularly useful in the analysis and design of compliant mechanisms.

Parametric Deflection Approximations for End-Loaded, Large-Deflection Beams in Compliant Mechanisms

1992 ◽  
Author(s):  
Larry L. Howell ◽  
Ashok Midha
Keyword(s):  
Closed Form ◽  
Large Deflection ◽  
Numerical Solutions ◽  
Compliant Mechanisms ◽  
Elliptic Integral ◽  
Cantilever Beams ◽  
Simple Method ◽  
Body Angle ◽  
Analysis And Design ◽  
Integral Solutions

Abstract Geometric nonlinearities often complicate the analysis of systems containing large-deflection members. The time and resources required to develop closed-form or numerical solutions nave inspired the development of a simple method of approximating the deflection path of end-loaded, large-deflection cantilever beams. The path coordinates are parameterized in a single parameter, called the pseudo-rigid-body angle. The approximations are accurate to within 0.5% of the closed-form elliptic integral solutions. A physical model is associated with the method, and may be used to simplify complex problems. The method proves to be particularly useful in the analysis and design of compliant mechanisms.

Buckling Analysis of Hollow Microneedle in Transdermal Drug Delivery

2016 ◽  
Author(s):  
N. Raja Rajeswari ◽  
P. Malliga ◽  
B. K. Gnanavel
Keyword(s):  
Drug Delivery ◽  
Transdermal Drug Delivery ◽  
Reaction Force ◽  
Vital Role ◽  
Buckling Analysis ◽  
Buckling Load ◽  
Insertion Force ◽  
Element Analysis ◽  
Critical Buckling Load ◽  
Hollow Microneedle

In biomedical field, the microneedles have gained popularity in the transdermal drug delivery applications. A hollow out-of-plane microneedle with bevel shaped tip, made up of silicon material is considered in this paper. The safe insertion of such microneedles into the soft tissue without breakage plays a vital role in the design of microneedles. The primary mode of failure often found in microneedles is buckling. When the microneedle is applied with an insertion force (F) larger than the critical buckling load (Pcr), it may suffer from buckling. In this paper, the buckling analysis of silicon microneedle is performed using Finite Element Analysis. The equilibrium equation of Love’s (1944) thin rod theory is used to study the buckling effect of microneedle. A non-linear Eigen value buckling analysis of the hollow microneedle is performed. The fundamental mode 1 and the critical mode 813 are discussed. The deflection, stresses and reaction force are analysed for both the modes. The critical buckling load (Pcr) is determined to be 0.39 N and if the microneedle is applied with insertion force within this value of critical buckling load, it avoids buckling. Therefore, this critical buckling load is taken as a conservative result for designing the microneedle.

Large-Deflection Analysis of General Beams in Contact-Aided Compliant Mechanisms Using Chained Pseudo-Rigid-Body Model

2020 ◽  
Vol 12 (3) ◽  
Author(s):  
Mohui Jin ◽  
Zhou Yang ◽  
Collin Ynchausti ◽  
Benliang Zhu ◽  
Xianmin Zhang ◽  
...  
Keyword(s):  
Rigid Body ◽  
Large Deflection ◽  
Compliant Mechanisms ◽  
Reaction Force ◽  
Curved Beams ◽  
Nonlinear Method ◽  
Analysis And Design ◽  
Body Model ◽  
Rigid Body Model ◽  
Force Moment

Abstract The nonlinear analysis and design of contact-aided compliant mechanisms (CCMs) are challenging. This paper presents a nonlinear method for analyzing the deformation of general beams that contact rigid surfaces in CCMs. The large deflection of the general beam is modeled by using the chained pseudo-rigid-body model. A geometry constraint from the contact surface is developed to constrain the beam’s deformed configuration. The contact analysis problem is formulated based on the principle of minimum potential energy and solved using an optimization algorithm. Besides, a novel technique based on the principle of work and energy is proposed to calculate the reaction force/moment of displacement-loaded cases. Several analysis examples of the compliant mechanisms with straight or curved beams are used to verify the proposed method. The results show that the proposed method and technique can evaluate the deformation of beam-based CCMs and the reaction force/moment with acceptable accuracy, respectively.

A Simplified Design Model for Modular Steel Buildings Subject to Vapor Cloud Explosions (VCEs)

2020 ◽  
Vol 14 ◽  
Author(s):  
Osama Bedair
Keyword(s):  
Dynamic Response ◽  
Minimum Cost ◽  
Design Parameters ◽  
Front Wall ◽  
Steel Buildings ◽  
Element Analysis ◽  
Analysis And Design ◽  
Vapor Cloud ◽  
Building Components ◽  
Analytical Expressions

Background: Modular steel buildings (MSB) are extensively used in petrochemical plants and refineries. Limited guidelines are available in the industry for analysis and design of (MSB) subject to accidental vapor cloud explosions (VCEs). Objectives: The paper presents simplified engineering model for modular steel buildings (MSB) subject to accidental vapor cloud explosions (VCEs) that are extensively used in petrochemical plants and refineries. Method: A Single degree of freedom (SDOF) dynamic model is utilized to simulate the dynamic response of primary building components. Analytical expressions are then provided to compute the dynamic load factors (DLF) for critical building elements. Recommended foundation systems are also proposed to install the modular building with minimum cost. Results: Numerical results are presented to illustrate the dynamic response of (MSB) subject to blast loading. It is shown that (DLF)=1.6 is attained at (td/t)=0.4 for front wall (W1) with (td/T)=1.25. For side walls (DLF)=1.41 and is attained at (td/t)=0.6. Conclusions: The paper presented simplified tools for analysis and design of (MSB) subject accidental vapor cloud blast explosions (VCEs). The analytical expressions can be utilized by practitioners to compute the (MSB) response and identify the design parameters. They are simple to use compared to Finite Element Analysis.

scholarly journals APPLICATION OF DOMAIN INTEGRATED DESIGN METHODOLOGY FOR BIO-INSPIRED DESIGN- A CASE STUDY OF SUTURE PIN DESIGN

2021 ◽  
Vol 1 ◽  
pp. 487-496
Author(s):  
Pavan Tejaswi Velivela ◽  
Nikita Letov ◽  
Yuan Liu ◽  
Yaoyao Fiona Zhao
Keyword(s):  
Cross Sections ◽  
Design Methodology ◽  
Reaction Force ◽  
Integrated Design ◽  
Total Deformation ◽  
Insertion Force ◽  
Force Reaction ◽  
The Moment ◽  
Work Done

AbstractThis paper investigates the design and development of bio-inspired suture pins that would reduce the insertion force and thereby reducing the pain in the patients. Inspired by kingfisher's beak and porcupine quills, the conceptual design of the suture pin is developed by using a unique ideation methodology that is proposed in this research. The methodology is named as Domain Integrated Design, which involves in classifying bio-inspired structures into various domains. There is little work done on such bio-inspired multifunctional aspect. In this research we have categorized the vast biological functionalities into domains namely, cellular structures, shapes, cross-sections, and surfaces. Multi-functional bio-inspired structures are designed by combining different domains. In this research, the hypothesis is verified by simulating the total deformation of tissue and the needle at the moment of puncture. The results show that the bio-inspired suture pin has a low deformation on the tissue at higher velocities at the puncture point and low deformation in its own structure when an axial force (reaction force) is applied to its tip. This makes the design stiff and thus require less force of insertion.

scholarly journals 3D Finite Element Analysis of Rotary Instruments in Root Canal Dentine with Different Elastic Moduli

2021 ◽  
Vol 11 (6) ◽  
pp. 2547 ◽  
Author(s):  
Carlo Prati ◽  
João Paulo Mendes Tribst ◽  
Amanda Maria de Oliveira Dal Piva ◽  
Alexandre Luiz Souto Borges ◽  
Maurizio Ventre ◽  
...  
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Root Canal ◽  
Elastic Moduli ◽  
Reaction Force ◽  
Von Mises Stress ◽  
Elastic Behavior ◽  
Element Analysis ◽  
Heat Treated ◽  
Von Mises

The aim of the present investigation was to calculate the stress distribution generated in the root dentine canal during mechanical rotation of five different NiTi endodontic instruments by means of a finite element analysis (FEA). Two conventional alloy NiTi instruments F360 25/04 and F6 Skytaper 25/06, in comparison to three heat treated alloys NiTI Hyflex CM 25/04, Protaper Next 25/06 and One Curve 25/06 were considered and analyzed. The instruments’ flexibility (reaction force) and geometrical features (cross section, conicity) were previously investigated. For each instrument, dentine root canals with two different elastic moduli(18 and 42 GPa) were simulated with defined apical ratios. Ten different CAD instrument models were created and their mechanical behaviors were analyzed by a 3D-FEA. Static structural analyses were performed with a non-failure condition, since a linear elastic behavior was assumed for all components. All the instruments generated a stress area concentration in correspondence to the root canal curvature at approx. 7 mm from the apex. The maximum values were found when instruments were analyzed in the highest elastic modulus dentine canal. Strain and von Mises stress patterns showed a higher concentration in the first part of curved radius of all the instruments. Conventional Ni-Ti endodontic instruments demonstrated higher stress magnitudes, regardless of the conicity of 4% and 6%, and they showed the highest von Mises stress values in sound, as well as in mineralized dentine canals. Heat-treated endodontic instruments with higher flexibility values showed a reduced stress concentration map. Hyflex CM 25/04 displayed the lowest von Mises stress values of, respectively, 35.73 and 44.30 GPa for sound and mineralized dentine. The mechanical behavior of all rotary endodontic instruments was influenced by the different elastic moduli and by the dentine canal rigidity.

scholarly journals Experimental Study and Development of Design Formula for Estimating the Ultimate Strength of Curved Plates

2021 ◽  
Vol 11 (5) ◽  
pp. 2379
Author(s):  
Jeong-Hyeon Kim ◽  
Doo-Hwan Park ◽  
Seul-Kee Kim ◽  
Myung-Sung Kim ◽  
Jae-Myung Lee
Keyword(s):  
Aspect Ratio ◽  
Ultimate Strength ◽  
Large Deflection ◽  
Slenderness Ratio ◽  
Compressive Load ◽  
Element Analysis ◽  
Shipbuilding Industry ◽  
Design Formula ◽  
Deflection Analysis ◽  
Collapse Behavior

The curved plate has been extensively used as a structural member in many industrial fields, especially the shipbuilding industry. The present study investigated the ultimate strength and collapse behavior of the simply supported curved plate under a longitudinal compressive load. To do this, experimental apparatuses for evaluating the buckling collapse test of the curved plates was developed. Then, a series of buckling collapse experiments was carried out by considering the flank angle, slenderness ratio, and aspect ratio of plates. To examine the fundamental buckling and collapse behavior of the curved plate, elastoplastic large deflection analysis was performed using the commercial finite element analysis program. On the basis of both the experimental and FE analysis, the effects of the flank angle, slenderness ratio, and aspect ratio on the characteristics of the buckling and collapse behavior of the curved plates are discussed. Finally, the empirical design formula for predicting the ultimate strength of curved plates was derived. The proposed empirical formula is a good indicator for estimating the behavior of the curved plate.

Evaluation of Equivalent Spring Stiffness for Use in a Pseudo-Rigid-Body Model of Large-Deflection Compliant Mechanisms

1994 ◽  
Author(s):  
Larry L. Howell ◽  
Ashok Midha
Keyword(s):  
Rigid Body ◽  
Large Deflection ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Spring Stiffness ◽  
Model Concept ◽  
Analysis And Design ◽  
Body Model ◽  
Rigid Body Model ◽  
Body Joints

Abstract Compliant mechanisms gain some or all of their mobility from the flexibility of their members rather than from rigid-body joints only. More efficient and usable analysis and design techniques are needed before the advantages of compliant mechanisms can be fully utilized. In an earlier work, a pseudo-rigid-body model concept, corresponding to an end-loaded geometrically nonlinear, large-deflection beam, was developed to help fulfill this need. In this paper, the pseudo-rigid-body equivalent spring stiffness is investigated and new modeling equations are proposed. The result is a simplified method of modeling the force/deflection relationships of large-deflection members in compliant mechanisms. Flexible segments which maintain a constant end angle are discussed, and an example mechanism is analyzed. The resulting models are valuable in the visualization of the motion of large-deflection systems, as well as the quick and efficient evaluation and optimization of compliant mechanism designs.

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