Topology optimization of density type for a linear elastic body by using the second derivative of a KS function with respect to von Mises stress

2018 ◽  
Vol 58 (3) ◽  
pp. 935-953 ◽  
Author(s):  
Wares Chancharoen ◽  
Hideyuki Azegami
Keyword(s):  
Topology Optimization ◽  
Elastic Body ◽  
Von Mises Stress ◽  
Second Derivative ◽  
Linear Elastic ◽  
Linear Elastic Body ◽  
Von Mises ◽  
Ks Function

On the Motion of an Elastic Body Rolling/Sliding on an Elastic Substrate

1995 ◽  
Vol 117 (2) ◽  
pp. 308-314 ◽  
Author(s):  
A. Spector ◽  
R. C. Batra
Keyword(s):  
Elastic Body ◽  
Frictional Force ◽  
Three Dimensional ◽  
The Body ◽  
Elastic Substrate ◽  
Linear Elastic ◽  
Linear Elastic Body ◽  
Body Rolling ◽  
Applied Forces ◽  
Two Phases

The three-dimensional evolutionary problem of rolling/sliding of a linear elastic body on a linear elastic substrate is studied. The inertial properties of the body regarded as rigid are accounted for. By employing an asymptotic analysis, it is shown that the process can be divided into two phases: transient and quasistationary. An expression for the frictional force as a function of the externally applied forces and moments, and inertial properties of the body is derived. For an ellipsoid rolling/sliding on a linear elastic substrate, numerical results for the frictional force distribution, slip/adhesion subareas, and the evolution of the slip velocity are given.

scholarly journals Combined shape and topology optimization for minimization of maximal von Mises stress

2017 ◽  
Vol 55 (5) ◽  
pp. 1541-1557 ◽  
Author(s):  
Haojie Lian ◽  
Asger N. Christiansen ◽  
Daniel A. Tortorelli ◽  
Ole Sigmund ◽  
Niels Aage
Keyword(s):  
Topology Optimization ◽  
Von Mises Stress ◽  
Shape And Topology Optimization ◽  
And Topology ◽  
Von Mises

The Physical Meaning of Astatic Equilibrium in Saint-Venant’s Principle for Linear Elasticity

1969 ◽  
Vol 36 (3) ◽  
pp. 392-396 ◽  
Author(s):  
C. A. Berg
Keyword(s):  
Stress Field ◽  
Elastic Body ◽  
Long Range ◽  
Small Volume ◽  
Boundary Surface ◽  
Small Region ◽  
Main Body ◽  
Linear Elastic ◽  
Loading System ◽  
Linear Elastic Body

When a boundary loading which is not only self-equilibrated but has the additional property that the loading system remains self-equilibrated when all the forces are rotated through an arbitrary angle about their points of application (astatic equilibrium), is applied to a small region of the surface of a linear elastic body, the long range stress field produced by the loading is in general of smaller order (with respect to the radius of the loaded segment of the boundary) than would be the long range stress field produced by a loading system which was merely self-equilibrating but which would not continue to be self-equilibrating if each force were rotated (von Mises [3], Sternberg [6]). The physical distinctions between astatic equilibrium loadings and merely self-equilibrated loadings, and the physical reasons why astatic equilibrium loadings produce smaller long range stresses, are examined. It is pointed out that astatic equilibrium loadings always produce zero mean deformation in a linear elastic body and that, therefore, if a small volume element, in the neighborhood of a small patch of the boundary surface subject to astatic equilibrium loading were considered as an isolated body, this small volume would undergo no mean deformation and would be easier to fit back into the main body than if it had been subject to merely self-equilibrated loading which would have caused mean deformation.

scholarly journals Strength and stiffness analyses of standard and double mortise and tenon joints

BioResources ◽  
2020 ◽  
Vol 15 (4) ◽  
pp. 8249-8267
Author(s):  
Seid Hajdarevic ◽  
Murco Obucina ◽  
Elmedin Mesic ◽  
Sandra Martinovic
Keyword(s):  
Bending Moment ◽  
Von Mises Stress ◽  
Elastic Model ◽  
Proportional Limit ◽  
Linear Elastic ◽  
Mortise And Tenon ◽  
Strength And Stiffness ◽  
Experimental Values ◽  
Maximal Moment ◽  
Von Mises

This paper investigated the effect of the tenon length on the strength and stiffness of the standard mortise and tenon joints, as well of the double mortise and tenon joints, that were bonded by poly(vinyl acetate) (PVAc) and polyurethane (PU) glues. The strength was analyzed by measuring applied load and by calculating ultimate bending moment and bending moment at the proportional limit. Stiffness was evaluated by measuring displacement and by calculating the ratio of applied force and displacement along the force line. The results were compared with the data obtained by the simplified static expressions and numerical calculation of the orthotropic linear-elastic model. The results indicated that increasing tenon length increased the maximal moment and proportional moment of the both investigated joints types. The analytically calculated moments were increased more than the experimental values for both joint types, and they had generally lower values than the proportional moments for the standard tenon joints, as opposed to the double tenon joints. The Von Mises stress distribution showed characteristic zones of the maximum and increased stress values. These likewise were monitored in analytical calculations. The procedures could be successfully used to achieve approximate data of properties of loaded joints.

Topology optimization of structures subject to self-weight loading under stress constraints

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Renatha Batista dos Santos ◽  
Cinthia Gomes Lopes
Keyword(s):  
Topology Optimization ◽  
Stress Constraints ◽  
Topological Derivative ◽  
The Self ◽  
Von Mises Stress ◽  
Stress Constraint ◽  
Content Type ◽  
Derivative Method ◽  
Von Mises ◽  
Weight Loading

PurposeThe purpose of this paper is to present an approach for structural weight minimization under von Mises stress constraints and self-weight loading based on the topological derivative method. Although self-weight loading topology has been the subject of intense research, mainly compliance minimization has been addressed.Design/methodology/approachThe resulting minimization problem is solved with the help of the topological derivative method, which allows the development of efficient and robust topology optimization algorithms. Then, the derived result is used together with a level-set domain representation method to devise a topology design algorithm.FindingsNumerical examples are presented, showing the effectiveness of the proposed approach in solving a structural topology optimization problem under self-weight loading and stress constraint. When the self-weight loading is dominant, the presence of the regularizing term in the formulation is crucial for the design process.Originality/valueThe novelty of this research work lies in the use of a regularized formulation to deal with the presence of the self-weight loading combined with a penalization function to treat the von Mises stress constraint.

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