A Framework for Energy-Based Kinetostatic Modeling of Compliant Mechanisms

2017 ◽  
Author(s):  
Guimin Chen ◽  
Fulei Ma ◽  
Ruiyu Bai ◽  
Spencer P. Magleby ◽  
Larry L. Howell
Keyword(s):  
Strain Energy ◽  
Compliant Mechanisms ◽  
Modeling Framework ◽  
Geometric Nonlinearities ◽  
Complementary Strain ◽  
Minimum Strain Energy ◽  
Constraint Model ◽  
Future Work

Although energy-based methods have advantages over the Newtonian methods for kinetostatic modeling, the geometric nonlinearities inherent in deflections of compliant mechanisms preclude most of the energy-based theorems. Castigliano’s first theorem and the Crotti-Engesser theorem, which don’t require the problem being solved to be linear, are selected to construct the energy-based kinetostatic modeling framework for compliant mechanisms in this work. Utilization of these two theorems requires explicitly formulating the strain energy in terms of deflections and the complementary strain energy in terms of loads, which are derived based on the beam constraint model. The kinetostatic modeling of two compliant mechanisms are provided to demonstrate the effectiveness of using Castigliano’s first theorem and the Crotti-Engesser theorem with the explicit formulations in this framework. Future work will be focused on incorporating use of the principle of minimum strain energy and the principle of minimum complementary strain energy.

scholarly journals An Energy-Based Framework for Nonlinear Kinetostatic Modeling of Compliant Mechanisms Utilizing Beam Flexures

2021 ◽  
pp. 1-18
Author(s):  
Guimin Chen ◽  
Fulei Ma ◽  
Ruiyu Bai ◽  
Weidong Zhu ◽  
Spencer P Magleby ◽  
...  
Keyword(s):  
Strain Energy ◽  
Compliant Mechanisms ◽  
Modeling Framework ◽  
Geometric Nonlinearities ◽  
Complementary Strain ◽  
Constraint Model

Abstract Although energy-based methods have advantages over the Newtonian methods for kinetostatic modeling, the geometric nonlinearities inherent in deflections of compliant mechanisms preclude most of the energy-based theorems. Castigliano's first theorem and the Crotti-Engesser theorem, which don't require the problem being solved to be linear, are selected to construct the energy-based kinetostatic modeling framework for compliant mechanisms in this work. Utilization of these two theorems requires explicitly formulating the strain energy in terms of deflections and the complementary strain energy in terms of loads, which are derived based on the beam constraint model. The kinetostatic modeling of two compliant mechanisms are provided to demonstrate the effectiveness of the explicit formulations in this framework derived from Castigliano's first theorem and the Crotti-Engesser theorem.

Modeling Large Planar Deflections of Flexible Beams in Compliant Mechanisms Using Chained Beam-Constraint-Model1

2015 ◽  
Vol 8 (2) ◽  
Author(s):  
Fulei Ma ◽  
Guimin Chen
Keyword(s):  
Strain Energy ◽  
Large Deflection ◽  
Compliant Mechanisms ◽  
Research Community ◽  
New Method ◽  
Flexible Beam ◽  
Large Deflections ◽  
Flexible Beams ◽  
Versatile Tool ◽  
Constraint Model

Modeling large deflections has been one of the most fundamental problems in the research community of compliant mechanisms. Although many methods are available, there still exists a need for a method that is simple, accurate, and can be applied to a vast variety of large deflection problems. Based on the beam-constraint model (BCM), we propose a new method for modeling large deflections called chained BCM (CBCM), which divides a flexible beam into a few elements and models each element by BCM. The approaches for determining the strain energy stored in a deflected beam and the stress distributed on it are also presented within the framework of CBCM. Several typical examples were analyzed and the results show CBCMs capabilities of modeling various large deflections of flexible beams in compliant mechanisms. Generally, CBCM can serve as an efficient and versatile tool for solving large deflection problems in a variety of compliant mechanisms.

Structural Topology Optimization Using Frame Elements Based on the Complementary Strain Energy Concept for Eigen-Frequency Maximization

2005 ◽  
Author(s):  
Akihiro Takezawa ◽  
Shinji Nishiwaki ◽  
Kazuhiro Izui ◽  
Masataka Yoshimura
Keyword(s):  
Topology Optimization ◽  
Cross Sections ◽  
Strain Energy ◽  
Optimization Procedure ◽  
Optimization Method ◽  
Structural Topology ◽  
Energy Concept ◽  
Conceptual Design Phase ◽  
Complementary Strain ◽  
Topology Optimization Method

This paper discuses a new topology optimization method using frame elements for the design of mechanical structures at the conceptual design phase. The optimal configurations are determined by maximizing multiple eigen-frequencies in order to obtain the most stable structures for dynamic problems. The optimization problem is formulated using frame elements having ellipsoidal cross-sections, as the simplest case. Construction of the optimization procedure is based on CONLIN and the complementary strain energy concept. Finally, several examples are presented to confirm that the proposed method is useful for the topology optimization method discussed here.

The Behaviour of Multiple Loops in Torsion

1988 ◽  
Vol 15 (3) ◽  
pp. 149-156 ◽  
Author(s):  
R. A. Cavina ◽  
N. E. Waters
Keyword(s):  
Energy Method ◽  
Strain Energy ◽  
Vertical Axis ◽  
Experimental Measurements ◽  
Complementary Strain ◽  
Radial Axis ◽  
Strain Energy Method ◽  
Good Agreement

The angular stiffness of a multiple looped span, subject to rotation about a vertical axis (torsion) and also to rotation about a horizontal or radial axis (mesio-distal tilt), have been derived using the complementary (strain) energy method. Experimental measurements on enlarged models were in good agreement with the values calculated from the theoretical relationships obtained. The variations in angular stiffness resulting from changes in the loop height, width, and position of clinical sized loops are discussed.

Crack Driving Force in Anisotropic Media due to Non-Elastic Deformation

2004 ◽  
Vol 261-263 ◽  
pp. 75-80
Author(s):  
G.H. Nie ◽  
H. Xu
Keyword(s):  
Elastic Deformation ◽  
Driving Force ◽  
Strain Energy ◽  
Elastic Stress ◽  
Complex Function ◽  
Crack Driving Force ◽  
Special Cases ◽  
Degree Of Anisotropy ◽  
Minimum Strain Energy ◽  
Orthotropic Media

In this paper elastic stress field in an elliptic inhomogeneity embedded in orthotropic media due to non-elastic deformation is determined by the complex function method and the principle of minimum strain energy. Two complex parameters are expressed in a general form, which covers all characterizations of the degree of anisotropy for any ideal orthotropic elastic body. The stress acting on the long side of ellipse can be considered as a crack driving force and applied in failure and fatigue analysis of composites. For some special cases, the resulting solutions will reduce to the known results.

Modeling Large Spatial Deflections of Slender Bisymmetric Beams in Compliant Mechanisms Using Chained Spatial-Beam Constraint Model

2016 ◽  
Vol 8 (4) ◽  
Author(s):  
Guimin Chen ◽  
Ruiyu Bai
Keyword(s):  
Finite Element Analysis ◽  
Compliant Mechanisms ◽  
Research Community ◽  
Nonlinear Finite Element ◽  
Nonlinear Constraint ◽  
Element Analysis ◽  
Flexible Beams ◽  
Spatial Beams ◽  
Spatial Beam ◽  
Constraint Model

Modeling large spatial deflections of flexible beams has been one of the most challenging problems in the research community of compliant mechanisms. This work presents a method called chained spatial-beam constraint model (CSBCM) for modeling large spatial deflections of flexible bisymmetric beams in compliant mechanisms. CSBCM is based on the spatial-beam constraint model (SBCM), which was developed for the purpose of accurately predicting the nonlinear constraint characteristics of bisymmetric spatial beams in their intermediate deflection range. CSBCM deals with large spatial deflections by dividing a spatial beam into several elements, modeling each element with SBCM, and then assembling the deflected elements using the transformation defined by Tait–Bryan angles to form the whole deflection. It is demonstrated that CSBCM is capable of solving various large spatial deflection problems either the tip loads are known or the tip deflections are known. The examples show that CSBCM can accurately predict large spatial deflections of flexible beams, as compared to the available nonlinear finite element analysis (FEA) results obtained by ansys. The results also demonstrated the unique capabilities of CSBCM to solve large spatial deflection problems that are outside the range of ansys.

scholarly journals Reliability Based Analysis and Optimum Design of Laterally Loaded Piles

2017 ◽  
Author(s):  
Majid Movahedi Rad
Keyword(s):  
Limit Analysis ◽  
Strain Energy ◽  
Load Capacity ◽  
Optimization Procedure ◽  
Load Parameter ◽  
Plastic Limit ◽  
Laterally Loaded Piles ◽  
Plastic Limit Analysis ◽  
Complementary Strain ◽  
Laterally Loaded

In this study reliability based limit analysis is used to determine the ultimate capacity of laterally loaded piles.  The aim of this study is to evaluate the lateral load capacity of free-head and fixed-head long pile when plastic limit analysis is considered. In addition to the plastic limit analysis to control the plastic behaviour of the structure, uncertain bound on the complementary strain energy of the residual forces is also applied. This bound has significant effect for the load parameter. The solution to reliability-based problems is based on a direct integration technique and the uncertainties are assumed to follow Gaussian distribution. The optimization procedure is governed by the reliability index calculation.

scholarly journals Extension of Castigliano’s method for isotropic beams

2020 ◽  
Vol 231 (11) ◽  
pp. 4621-4640
Author(s):  
Juergen Schoeftner
Keyword(s):  
Shear Force ◽  
Strain Energy ◽  
Axial Stress ◽  
Bending Moment ◽  
Axial Direction ◽  
Present Contribution ◽  
Special Cases ◽  
Dummy Load ◽  
Complementary Strain ◽  
Castigliano’S Theorem

Abstract In the present contribution Castigliano’s theorem is extended to find more accurate results for the deflection curves of beam-type structures. The notion extension in the context of the second Castigliano’s theorem means that all stress components are included for the computation of the complementary strain energy, and not only the dominant axial stress and the shear stress. The derivation shows that the partial derivative of the complementary strain energy with respect to a scalar dummy parameter is equal to the displacement field multiplied by the normalized traction vector caused by the dummy load distribution. Knowing the Airy stress function of an isotropic beam as a function of the bending moment, the normal force, the shear force and the axial and vertical load distributions, higher-order formulae for the deflection curves and the cross section rotation are obtained. The analytical results for statically determinate and indeterminate beams for various load cases are validated by analytical and finite element results. Furthermore, the results of the extended Castigliano theory (ECT) are compared to Bernoulli–Euler and Timoshenko results, which are special cases of ECT, if only the energies caused by the bending moment and the shear force are considered. It is shown that lower-order terms for the vertical deflection exist that yield more accurate results than the Timoshenko theory. Additionally, it is shown that a distributed load is responsible for shrinking or elongation in the axial direction.

Prediction of Cylinder Flow Pressures in Mass-Flow Bins Using Minimum Strain Energy

1976 ◽  
Vol 98 (4) ◽  
pp. 1370-1374 ◽  
Author(s):  
A. G. McLean ◽  
P. C. Arnold
Keyword(s):  
Mass Flow ◽  
Strain Energy ◽  
Plane Flow ◽  
Geometry Design ◽  
Numerical Effort ◽  
Minimum Strain Energy ◽  
Flow Pressure ◽  
Energy Theory ◽  
Cylinder Flow ◽  
Complete Variation

Jenike, et al. [1] have presented a minimum strain energy theory to predict cylinder flow pressures in mass-flow bins. The complete variation of strain energy pressures is depicted by bounds requiring considerable numerical effort to develop for a specific cylinder geometry. Design charts are presented, but these are available for only two circular cylinder geometries. This paper summarizes and clarifies the minimum strain energy theory for predicting cylinder flow pressures. A single bound approximation which allows the magnitude of the peak flow pressure to be determined for both axisymmetric and plane flow cylinders is presented. This peak pressure may also be estimated by a single calculation of strain energy pressure. The usefulness and accuracy of these procedures are illustrated by reworking the example presented by Jenike, et al. [1].

Recent Results on the Elasticity Theory of Inclusions

1994 ◽  
Vol 47 (1S) ◽  
pp. S10-S17 ◽  
Author(s):  
Jin H. Huang ◽  
T. Mura
Keyword(s):  
Composite Materials ◽  
Work Hardening ◽  
Strain Energy ◽  
Volume Fraction ◽  
Exact Formula ◽  
Stress And Strain ◽  
Inclusion Problems ◽  
Elastic Fields ◽  
Work Hardening Rate ◽  
Minimum Strain Energy

A method drawing from variational method is presented for the purpose of investigating the behavior of inclusions and inhomogeneities embedded in composite materials. The extended Hamilton’s principle is applied to solve many problems pertaining to composite materials such as constitutive equations, fracture mechanics, dislocation theory, overall elastic moduli, work hardening and sliding inclusions. Especially, elastic fields of sliding inclusions and workhardening rate of composite materials are presented in closed forms. For sliding inclusion problems, the sliding is modeled by adding the Somigliana dislocations along a matrix-inclusion interface. Exact formula are exploited for both Burgers vector and the disturbances in stress and strain due to sliding. The resulting expressions are obtained by utilizing the principle of minimum strain energy. Finally, explicit expressions are obtained for work-hardening rate of composite materials. It is verified that the work-hardening rate and yielding stress are independent on the size of inclusions but are dependent on the shape and the volume fraction of inclusions.

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