Shape Optimization of Thin-walled Structures Based on a New Shell Element and Uniform Strain Energy Density Criterion

2009 ◽  
Author(s):  
P. Khosravi ◽  
R. Sedaghati ◽  
R. Ganesan
Keyword(s):  
Energy Density ◽  
Shape Optimization ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Shell Element ◽  
Uniform Strain ◽  
Thin Walled Structures ◽  
Thin Walled

Structural optimization of thin-walled tubular trusses using a virtual strain energy density approach

2006 ◽  
Vol 44 (2) ◽  
pp. 235-246 ◽  
Author(s):  
Panagiotis A. Makris ◽  
Christopher G. Provatidis ◽  
Demetrios T. Venetsanos
Keyword(s):  
Energy Density ◽  
Structural Optimization ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Thin Walled ◽  
Virtual Strain Energy Density

New aspects of the trabecular bone remodeling regulatory model resulting from the shape optimization studies

2019 ◽  
Vol 234 (3) ◽  
pp. 282-288
Author(s):  
Michał Nowak ◽  
Jan Sokołowski ◽  
Antoni Żochowski
Keyword(s):  
Energy Density ◽  
Shape Optimization ◽  
Trabecular Bone ◽  
Bone Remodeling ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Natural Phenomenon ◽  
Bone Surface ◽  
Clinical Observations ◽  
Trabecular Bone Remodeling

The trabecular bone can adapt its form to mechanical loads and form structures that are both lightweight and very stiff. In this sense, it is a problem similar to structural optimization, especially topology optimization. The natural phenomenon leading to mechanical optimization of the bone structures is called trabecular bone remodeling. The main assumption and the benchmark for the numerical models of the phenomenon is the observation that the strain energy density on the structural surface is constant. This constant value corresponds to the homeostatic strain energy density, the state of bone tissue with a perfect balance of the loss, and gain of the bone mass. We assumed that the trabecular bone can form an optimal structure. The idea behind the investigation is to carry out studies on the ground of mechanics and to interpret clinical observations in the context of the results obtained from the optimization studies. In this way, clinical observations have been confirmed by strict arguments based on mechanics, leading to the unequivocal conclusion that equalization of the strain energy density on the trabecular bone surface allows minimizing the strain energy in the whole structure of the bone. This proves the veracity of the assumption that the remodeling process leads to the formation of the structure with the highest stiffness. In addition, this article elaborates on two new aspects of the remodeling phenomenon resulting directly from the considerations in the field of shape optimization important for numerical simulation. The first one concerns the influence of surface curvature on the remodeling process. The second one concerns the role of the bone surface where different loads are analyzed. Both aspects show the need of actual trabecular bone geometry model for the simulation of the trabecular bone remodeling phenomenon.

scholarly journals Volume free strain energy density method for applications to blunt V-notches

2020 ◽  
Vol 28 ◽  
pp. 734-742
Author(s):  
Pietro Foti ◽  
Seyed Mohammad Javad Razavi ◽  
Liviu Marsavina ◽  
Filippo Berto
Keyword(s):  
Energy Density ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Density Method ◽  
Free Strain

scholarly journals On the application of the volume free strain energy density method to blunt V-notches under mixed mode condition

2021 ◽  
Vol 230 ◽  
pp. 111716
Author(s):  
Pietro Foti ◽  
Seyed Mohammad Javad Razavi ◽  
Majid Reza Ayatollahi ◽  
Liviu Marsavina ◽  
Filippo Berto
Keyword(s):  
Energy Density ◽  
Strain Energy Density ◽  
Mixed Mode ◽  
Strain Energy ◽  
Density Method ◽  
Free Strain

scholarly journals Alternative derivation of the higher-order constitutive model for six-parameter elastic shells

2021 ◽  
Vol 72 (2) ◽  
Author(s):  
Mircea Bîrsan
Keyword(s):  
Energy Density ◽  
Constitutive Model ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Shell Theory ◽  
Constitutive Relations ◽  
Three Dimensional ◽  
Classical Shell Theory ◽  
Three Dimensional Elasticity ◽  
General Method

AbstractIn this paper, we present a general method to derive the explicit constitutive relations for isotropic elastic 6-parameter shells made from a Cosserat material. The dimensional reduction procedure extends the methods of the classical shell theory to the case of Cosserat shells. Starting from the three-dimensional Cosserat parent model, we perform the integration over the thickness and obtain a consistent shell model of order $$ O(h^5) $$ O ( h 5 ) with respect to the shell thickness h. We derive the explicit form of the strain energy density for 6-parameter (Cosserat) shells, in which the constitutive coefficients are expressed in terms of the three-dimensional elasticity constants and depend on the initial curvature of the shell. The obtained form of the shell strain energy density is compared with other previous variants from the literature, and the advantages of our constitutive model are discussed.

Storing Energy in the Mechanical Domain

2014 ◽  
Vol 1679 ◽  
Author(s):  
O.G. Súchil ◽  
G. Abadal ◽  
F. Torres
Keyword(s):  
Energy Source ◽  
Energy Density ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Critical Strain ◽  
Substrate Surface ◽  
Maximum Load ◽  
Linear Buckling ◽  
Initial Ph ◽  
Self Powered

ABSTRACTSelf-powered microsystems as an alternative to standard systems powered by electrochemical batteries are taking a growing interest. In this work, we propose a different method to store the energy harvested from the ambient which is performed in the mechanical domain. Our mechanical storage concept is based on a spring which is loaded by the force associated to the energy source to be harvested [1]. The approach is based on pressing an array of fine wires (fws) grown vertically on a substrate surface. For the fine wires based battery, we have chosen ZnO fine wires due the fact that they could be grown using a simple and cheap process named hydrothermal method [2]. We have reported previous experiments changing temperature and initial pH of the solution in order to determine the best growth [3]. From new experiments done varying the compounds concentration the best results of fine wires were obtained. To characterize these fine wires we have considered that the maximum load we can apply to the system is limited by the linear buckling of the fine wires. From the best results we obtained a critical strain of εc = 3.72 % and a strain energy density of U = 11.26 MJ/m3, for a pinned-fixed configuration [4].

On the Crack Initiated from the Bi-Material Notch Tip

2010 ◽  
Vol 452-453 ◽  
pp. 441-444 ◽  
Author(s):  
Tomáš Profant ◽  
Jan Klusák ◽  
Michal Kotoul
Keyword(s):  
Energy Density ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Local Minimum ◽  
Plane Elasticity ◽  
Mean Value ◽  
Tangential Stresses ◽  
Density Factor ◽  
The Mean ◽  
Energy Density Factor

The bi-material notch composed of two orthotropic parts is considered. The radial and tangential stresses and strain energy density is expressed using the Stroh-Eshelby-Lekhnitskii formalism for the plane elasticity. The potential direction of the crack initiation is determined from the maximum mean value of the tangential stresses and local minimum of the mean value of the generalized strain energy density factor in both materials. Matched asymptotic procedure is used to derive the change of potential energy for the debonding crack and the crack initiated in the determined direction.

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