A (3,2) reduced degree-of-freedom unified zigzag laminated beam theory

2020 ◽  
Vol 77 ◽  
pp. 1474-1496 ◽  
Author(s):  
Tianyu Li
Keyword(s):  
Beam Theory ◽  
Degree Of Freedom ◽  
Laminated Beam

Flexure-Based Two Degree-of-Freedom Legs for Walking Microrobots

2006 ◽  
Author(s):  
Ankur M. Mehta ◽  
Kristofer S. J. Pister
Keyword(s):  
Analytical Model ◽  
Design Space ◽  
Beam Theory ◽  
Degree Of Freedom ◽  
Bernoulli Beam ◽  
Comb Drive ◽  
Walking Gait ◽  
Euler Bernoulli Beam ◽  
Force Displacement ◽  
Two Degree Of Freedom

This work examines the design of legs for a walking microrobot. The parameterized force-displacement relationships of planar serpentine flexure-based two degree-of-freedom legs are analyzed. An analytical model based on Euler-Bernoulli beam theory is developed to explore the design space, and is subsequently refined to include contact between adjacent beams. This is used to determine a successful leg geometry given dimensional constraints and actuator limitations. Standard comb drive actuators that output 100 μN of force over a 15 μm bi-directional throw are shown able to drive a walking gait with three legs on a 1 cm2 silicon die microrobot. If the comb drive suspensions cannot withstand the generated reaction moments, an alternate pivot-based leg linkage is proposed.

scholarly journals Mechanical models in computational form finding of bending-active structures

2018 ◽  
Vol 33 (2) ◽  
pp. 86-97 ◽  
Author(s):  
Carlos Lázaro ◽  
Juan Bessini ◽  
Salvador Monleón
Keyword(s):  
Three Dimensional ◽  
Beam Theory ◽  
Task Type ◽  
Degree Of Freedom ◽  
Complex Nature ◽  
Dynamic Relaxation ◽  
Form Finding ◽  
Beam Elements ◽  
Active Structures ◽  
Computational Form

This article reviews the different aspects involved in computational form finding of bending-active structures based on the dynamic relaxation technique. Dynamic relaxation has been applied to form-finding problems of bending-active structures in a number of references. Due to the complex nature of large spatial deformations of flexible beams, the implementation of suitable mechanical beam models in the dynamic relaxation algorithm is a non-trivial task. Type of discretization and underlying beam theory have been identified as key aspects for numerical implementations. References can be classified into two groups depending on the selected discretization: finite-difference-like and finite-element-like. The first group includes 3- and 4-degree-of-freedom implementations based on increasingly complex beam models. The second gathers 6-degree-of-freedom discretizations based on co-rotational three-dimensional Kirchhoff–Love beam elements and geometrically exact Reissner–Simo beam elements. After reviewing and comparing implementation details, the advantages and drawbacks of each group have been discussed, and open aspects for future work have been pointed out.

Local Delamination Buckling of a Laminated Beam due to Three-Point Bending

2010 ◽  
Vol 132 (3) ◽  
Author(s):  
M. Toya ◽  
K. Fukagawa ◽  
M. Aritomi ◽  
M. Oda ◽  
T. Miyauchi
Keyword(s):  
Applied Load ◽  
Beam Theory ◽  
Critical Value ◽  
Laminated Beam ◽  
Three Point Bending ◽  
Tensile Forces ◽  
Delamination Buckling ◽  
Perfect Contact ◽  
Layered Beam ◽  
Crack Faces

Asymmetric three-point bending of a layered beam containing an interior interface crack is analyzed on the basis of the classical beam theory. Axial compressive and tensile forces are induced by bending in the parts of the beam above and below the delamination, and they are determined by modeling the cracked part as two lapped beams jointed together at the corners of both beams. When the magnitude of the applied load is small, the beam deflects, retaining the mutual contact of whole crack faces, but as the applied load reaches a critical value, local delamination buckling of the compressed part occurs. The relation between the magnitude of the applied load and the deflection at the point of load application is found to be nearly bilinear. The validity of this prediction is confirmed by experiments. It is also shown that once the delamination buckling occurs, the energy release rate generally becomes larger as compared with the case of a perfect contact of delaminated surfaces.

A Delamination in a Three Layers Laminated Beam Subjected to Thermal Gradient

2013 ◽  
Vol 845 ◽  
pp. 367-371
Author(s):  
Mikio Oda ◽  
Binti Ibrahim Anis Farhana ◽  
Y. Nakamura
Keyword(s):  
Temperature Gradient ◽  
Thermal Gradient ◽  
Numerical Solutions ◽  
Beam Theory ◽  
Relative Displacement ◽  
Critical Value ◽  
Laminated Beam ◽  
Axial Forces ◽  
Delamination Buckling ◽  
Crack Faces

A laminated beam containing an initial delamination subjected to thermal gradient is analyzed on the basis of classical beam theory. The axial forces are induced in the parts of the constituent beams above and below the delamination. For the case where crack faces are open, a nonlinear equation for determining the in-plane forces is derived by modeling the delaminated part as two lapped beams hinged at both ends, and by imposing the compatibility condition of the deformations of the two beams. Numerical solutions are obtained for some model beams. It is shown that the relative displacement at the center of the delamination increases gradually with the increase very rapidly, i.e., local delamination buckling occurs. Energy release rate is small for temperature gradient below the critical value, but it takes a large value when the temperature gradient is increased beyond the critical value.

Free Vibration of Cross Ply Laminated Beams with Multiple Distributed Piezoelectric Actuators

2012 ◽  
Vol 28 (1) ◽  
pp. 217-227 ◽  
Author(s):  
A. A. Khdeir ◽  
E. Darraj ◽  
O. J. Aldraihem
Keyword(s):  
Free Vibration ◽  
Equations Of Motion ◽  
Beam Theory ◽  
Piezoelectric Actuators ◽  
Mode Shapes ◽  
Beam Model ◽  
Laminated Beams ◽  
State Space Approach ◽  
Laminated Beam ◽  
Beam Surface

ABSTRACTAnalytical solution is obtained for the free vibration of cross-ply laminated beams with multiple distributed extension piezoelectric actuators. The piezoelectric actuators are bonded at local position on the beam surface. The beam structure can contain one pair or two pairs or n pairs of piezoelectric actuators and it can be symmetric or unsymmetric about its mid-plane. The equations of motion and associated boundary conditions are derived for the beam model using Hamilton's principle. The state-space approach is used to find accurate natural frequencies and mode shapes for arbitrary combinations of boary conditions. The exact analytical solutions obtained are illustrated numerically in a number of figures revealing the influences of varying some parameters for the symmetric and unsymmetric cross-ply laminated beam for different type of piezoelectric actuators cases. The first order shear deformation beam theory (FOBT) is used to present the effect of actuators position and length on the nondimensional frequencies when one pair and two pairs of piezoelectric actuators are bonded at a local position on the beam surface.

Modeling and Analysis of an Electrically Actuated Microbeam Based on Nonclassical Beam Theory

2014 ◽  
Vol 9 (3) ◽  
Author(s):  
Pierpaolo Belardinelli ◽  
Stefano Lenci ◽  
Maurizio Brocchini
Keyword(s):  
Correction Term ◽  
Differential Quadrature Method ◽  
Gradient Elasticity ◽  
Beam Theory ◽  
Static Solution ◽  
Dynamical Problem ◽  
Degree Of Freedom ◽  
Electric Voltage ◽  
Modeling And Analysis ◽  
Fringing Field

This work investigates the mechanical behavior of a clamped-clamped microbeam modeled within the framework of the strain-gradient elasticity theory. The governing equation of motion gives proper account of both the effect of the nonlinear midplane stretching and of an applied axial load. An electric-voltage difference, introducing into the model a further source of nonlinearity, is considered, including also a correction term for fringing field effects. The electric force acting on the microbeam is rearranged by means of the Chebyshev method, verifying the accuracy of the proposed approximation. The results show that a uniform error on the whole domain can be achieved. The static solution is obtained by a numerical differential quadrature method. The paper looks into the variation of the maximal deflection of the microbeam with respect to several parameters. Study of the pull-in limit on the high-order material parameters introduced by the nonclassical approach and a comparison with respect to the classical beam theory are also carried out. The numerical simulation indicates that the static response is larger, affected by the use of a nonclassical theory near the pull-in instability regime. The dynamical problem is, finally, analyzed, deriving the multi degree-of-freedom problem through a Galerkin-based approach. The study on the single degree-of-freedom model enables us to note the large influence of the nonlinear terms.

A Laminated Beam Theory With Interlayer Slip

1984 ◽  
Vol 51 (3) ◽  
pp. 551-559 ◽  
Author(s):  
H. Murakami
Keyword(s):  
Virtual Work ◽  
Sandwich Beam ◽  
Beam Theory ◽  
Transverse Shear Strain ◽  
Beam Model ◽  
Euler Beam ◽  
Concentrated Load ◽  
Laminated Beam ◽  
Wide Range ◽  
Interlayer Slip

A Timoshenko beam theory with built-in interlayer slip is developed to facilitate analytical means of simulating the effect of interlayer slip on the stiffness degradation of laminated beam structures. The proposed theory is unique in the sense that any well-structures interlay slip law can be adopted in the beam model. Based on the principle of virtual work, well-posed boundary value problems of the proposed beam theory are defined. It is shown that the proposed theory reduces to the existing Bernoulli-Euler beam theory with interlayer slip by introducing the kinematic constraint of zero transverse shear strain. As a demonstration of the theory the load-deflection curves of a simply supported sandwich beam subjected to a concentrated load at the center are computed for several characteristic interlayer slip laws. It is found that the proposed model has the capability of simulating the deformation of beams with wide range of interlayer bond qualities, from interface with perfect bond to interface without connectors.

Sign in / Sign up

Export Citation Format

Share Document