Solutions of the interfacial shear and normal stresses in plate flexural-strengthened beams based on different complementary strain energy assumptions

2021 ◽  
Vol 229 ◽  
pp. 111567
Author(s):  
Phe Van Pham
Keyword(s):  
Strain Energy ◽  
Interfacial Shear ◽  
Normal Stresses ◽  
Complementary Strain

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.

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.

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.

Continuous Microindentation and Microscratch Measurements of Metal-Ceramic Adhesive strengths

1991 ◽  
Vol 239 ◽  
Author(s):  
S. Venkataraman ◽  
D. L. Kohlstedt ◽  
W. W. Gerberich
Keyword(s):  
Fracture Toughness ◽  
Strain Energy ◽  
Strain Energy Release Rate ◽  
Strain Energy Release ◽  
Interfacial Fracture ◽  
Interfacial Shear ◽  
Work Of Adhesion ◽  
Interfacial Fracture Toughness ◽  
Heat Treated ◽  
Metal Ceramic

ABSTRACTTo investigate the effect of heat-treatment on the adhesion of Pt thin films to NiO substrates, the strain energy release rate, interfacial fracture toughness and interfacial shear strength were determined from continuous microscratch and continuous microindentation experiments. Samples were prepared by sputtering Pt onto single crystals of NiO, followed by a heat-treatment at temperatures of 300, 500 and 800°C and an oxygen partial pressure of either 0.21 or 10-5 atm. Continuous microscratch tests were performed by driving a conical indenter with either a 1 or 5 μm tip radius simultaneously into and across the Pt film. From the magnitude of the critical load at the point of film delamination and the area of the delaminated piece of the thin film, the strain energy release rate (practical work of adhesion) and interfacial fracture toughness were calculated. The practical work of adhesion and interfacial fracture toughness increased from 0.2 J/m2 and 0.2 MPa√m, respectively, for as-sputtered samples to 4.6 J/m2 and 1 MPa√m for samples heat-treated at 500°C and 10-5 atm. Preliminary analysis of continuous microindentation results for Pt/NiO samples yielded interfacial shear strengths of 270 MPa for as-sputtered samples and 725 MPa for samples heat-treated at 500°C and 10-5 atm. While these values are in good agreement with those determined by other methods for metal-ceramic systems, there are sufficient differences in test method for a single system to require additional analysis of the proposed models.

An Expression for the Strain Energy of Laminated Composite Thin Shells

1995 ◽  
Vol 23 (2) ◽  
pp. 169-177 ◽  
Author(s):  
P. C. Tse ◽  
T. C. Lai
Keyword(s):  
Strain Energy ◽  
Laminated Composite ◽  
Local Stress ◽  
Thin Shells ◽  
Stress And Strain ◽  
Energy Storage Devices ◽  
Storage Devices ◽  
Linear Elastic ◽  
Complementary Strain ◽  
Indeterminate Structures

An expression for the complementary strain energy of a linear elastic laminated composite thin-walled structure is presented which describes the energy in terms of midplane properties and subsequently stress and moment resultants rather than local stress and strain values. This expression is particularly useful for the analysis of statically indeterminate structures and energy storage devices such as springs.

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