scholarly journals Deformation Stress State of Elastic Bodies

10.14311/660 ◽  
2005 ◽  
Vol 45 (1) ◽  
Author(s):  
J. Skokánek
Keyword(s):  
Stress State ◽  
Safety Margin ◽  
Theory Of Elasticity ◽  
State Theory ◽  
Elastic Bodies ◽  
Deformable Bodies ◽  
Internal Forces ◽  
Deformation Force ◽  
Deformation Stress ◽  
Solid Bodies

The theory of the deformation stress state is based on the actual corpuscular structure of matter characterized in terms of mechanics by the fact that an increase in the distance of two adjacent atoms is accompanied by the origin of an attractive force and a reduction in their distance by the origin of a repulsive force. These forces differ significantly from the classical internal forces, which are the forces of the mechanics of perfectly solid bodies. These express the equilibrium of forces with reference to the given area within the loaded body, and have no direct deformation effect. This paper defines the quantities of the deformation stress state – the deformation force and the deformation stress – the direct manifestation of which is a deformation. The author introduces the term of deformation stress state theory (DSS theory) to the field of the theory of elasticity dealing with the stress state of deformable bodies. The quantities and the equations of this theory also form the basis for the formulation of the theory of failure, which makes it possible to determine reliably the safety margin and the strength of a multiaxially loaded body from the stress state described by the static quantities (stress tensor) and uniaxial strength. 

A Finite Element for the Analysis of Shell Intersections

1996 ◽  
Vol 118 (4) ◽  
pp. 399-406 ◽  
Author(s):  
W. J. Koves ◽  
S. Nair
Keyword(s):  
Finite Element ◽  
Stress State ◽  
Three Dimensional ◽  
Shell Element ◽  
Theory Of Elasticity ◽  
Shell Elements ◽  
Asme Code ◽  
Form Theory ◽  
Computation Scheme ◽  
Shell Intersections

A specialized shell-intersection finite element, which is compatible with adjoining shell elements, has been developed and has the capability of physically representing the complex three-dimensional geometry and stress state at shell intersections (Koves, 1993). The element geometry is a contoured shape that matches a wide variety of practical nozzle configurations used in ASME Code pressure vessel construction, and allows computational rigor. A closed-form theory of elasticity solution was used to compute the stress state and strain energy in the element. The concept of an energy-equivalent nodal displacement and force vector set was then developed to allow complete compatibility with adjoining shell elements and retain the analytical rigor within the element. This methodology provides a powerful and robust computation scheme that maintains the computational efficiency of shell element solutions. The shell-intersection element was then applied to the cylinder-sphere and cylinder-cylinder intersection problems.

scholarly journals NONLINEAR DEFORMATION-FORCE MODEL OF A CONCRETE BAR WITH NON-METALLIC COMPOSITE REINFORCEMENT IN THE GENERAL CASE OF A STRESSED STATE

2021 ◽  
Vol 3 (1) ◽  
pp. 6-26
Author(s):  
I. Karpiuk ◽  
◽  
Ye. Klymenko ◽  
V. Karpiuk ◽  
M. Karpiuk ◽  
...  
Keyword(s):  
Stress State ◽  
Stressed State ◽  
Bearing Capacity ◽  
Nonlinear Deformation ◽  
Complex Stress ◽  
Complex Stress State ◽  
Force Model ◽  
Metallic Composite ◽  
Aggressive Environment ◽  
Deformation Force

The article discusses a nonlinear deformation-force model of a concrete bar structure with a non-metallic composite reinforcement (NKA-FRP) in the general case of a stressed state, when all four internal force factors from an external load (namely, bending and twisting moments, transverse and longitudinal forces). A sufficiently deep and meaningful analysis of well-known studies on the selected topic is given. It has been established that the proposed nonlinear deformation-force model of a bar structure with FRP in the general case of a stressed state can be practically useful due to the possibility of its application in the design or reinforcement of beams, girders, columns and elements of rosette trusses of rectangular cross-section, which are operated under aggressive environmental conditions. This model can also be used to check the bearing capacity of existing FRP concrete bar structures, which operate not only under the influence of an aggressive environment, but also under conditions of a complex stress-strain state. In the course of the research, an algorithm was developed for determining the bearing capacity of the design section of a concrete rod with FRP under its complex stress state. General physical relations for the design section are given in the form of a stiffness matrix. The algorithm for calculating a concrete bar with FRP consists of a block for inputting the initial data, the main part, auxiliary subroutines for checking the conditions for increasing the load vector and depletion of the bearing capacity, as well as a block for printing the calculation results. At each stage of a simple static stepwise increasing load, the calculation is carried out by performing a certain number of iterations until the accuracy of determining all components of the deformation vector satisfies a certain predetermined value. The features and patterns of changes in normal and tangential stresses, generalized linear and angular deformations, as well as the equations of equilibrium of a concrete bar with FRP, which operates under the influence of an aggressive environment under conditions of a complex stress state, are also considered.

Protein Forced Unfolding and Its Effects on the Finite Deformation Stress-Strain Behavior of Biomacromolecular Solids

2005 ◽  
Vol 874 ◽  
Author(s):  
H. Jerry Qi ◽  
Christine Ortiz ◽  
Mary C. Boyce
Keyword(s):  
Constitutive Model ◽  
Single Molecule ◽  
Biological Networks ◽  
Finite Deformation ◽  
State Theory ◽  
Force Extension ◽  
Stress Strain ◽  
Strain Behavior ◽  
Mechanics Model ◽  
Deformation Stress

AbstractMany proteins have been experimentally observed to exhibit a force-extension behavior with a characteristic repeating pattern of a nonlinear rise in force with imposed displacement to a peak, followed by a significant force drop upon reaching the peak (a “saw-tooth” profile) due to successive unfolding of modules during extension. This behavior is speculated to play a governing role in biological and mechanical functions of natural materials and biological networks composed of assemblies of such protein molecules. In this paper, a constitutive model for the finite deformation stress-strain behavior of crosslinked networks of modular macromolecules is developed. The force-extension behavior of the individual modular macromolecule is represented using the Freely Jointed Chain (FJC) statistical mechanics model together with a two-state theory to capture unfolding. The single molecule behavior is then incorporated into a formal continuum mechanics framework to construct a constitutive model. Simulations illustrate a relatively smooth “yield”-like stress-strain behavior of these materials due to activate unfolding in these microstructures.

Deformation, Stress State, and Thermodynamic Force for a Transforming Spherical Inclusion in an Elastic-Plastic Material

2000 ◽  
Vol 67 (4) ◽  
pp. 793-796 ◽  
Author(s):  
F. D. Fischer ◽  
E. R. Oberaigner
Keyword(s):  
Stress State ◽  
Volume Change ◽  
Plastic Material ◽  
Spherical Inclusion ◽  
Parent Phase ◽  
Thermodynamic Force ◽  
Elastic Plastic ◽  
Thermodynamic Forces ◽  
Deformation Stress ◽  
Elastic Plastic Material

The progress of a transformed phase into an elastic-plastic parent phase is simulated by a growing sphere. The transformation is accompanied by a dilatational volume change. The strain and stress state in the full space is presented. In addition, the local and global energy terms are calculated. Finally the thermodynamic forces on the interface are derived. Also strain hardening is considered. [S0021-8936(00)00304-4]

Seismic Behavior of Shear Wall-Frame Systems Considering Foundation Stiffness

2017 ◽  
Vol 17 (03) ◽  
pp. 1750041 ◽  
Author(s):  
Bo Di ◽  
Xueyi Fu
Keyword(s):  
Seismic Behavior ◽  
Safety Margin ◽  
Bending Moment ◽  
Shear Wall ◽  
Internal Force ◽  
Shallow Foundation ◽  
Frame Structure ◽  
Base Shear ◽  
Internal Forces ◽  
Frame Systems

In this paper, the influence of foundation stiffness on the seismic behavior of shear wall-frame systems was investigated. First, a basic differential equation was established to account for the interaction between the foundation and superstructure. By solving the equation, the influence of foundation stiffness on the lateral stiffness, inter-story drift, and internal force distribution of the superstructure at the elastic stage was elucidated. Subsequently, the concept and method for determining the range of foundation stiffness suitable for shear wall-frame systems were proposed. By taking a 12-story shear wall-frame structure built on a shallow foundation as an example, a parametric study was performed for various frame-to-wall relative stiffness ratios and foundation stiffnesses. The effect of shallow foundation stiffness on the base shear distribution and energy dissipation of the superstructure was clarified, with results compared with those of the fixed-base model. The analysis results indicated that the degeneration of foundation stiffness due to earthquake damages will result in significant redistribution of internal forces, namely, the internal forces of the walls decrease, while those of the frames increase. In particular, the shear-force and bending moment of the bottom frame columns rise drastically, which may greatly reduce the safety margin and should be considered in practical design.

The Stress State in Inhomogeneous Elastic Beam at Combined Strength

2014 ◽  
Vol 501-504 ◽  
pp. 645-648 ◽  
Author(s):  
Vladimir I. Andreev ◽  
Elena V. Barmenkova ◽  
Alena V. Matveeva
Keyword(s):  
Inverse Problem ◽  
Stress State ◽  
Modulus Of Elasticity ◽  
Elastic Beam ◽  
Bending Moment ◽  
Optimization Method ◽  
Theory Of Elasticity ◽  
Simultaneous Action ◽  
Concentrated Force ◽  
Inhomogeneous Bodies

In paper describes a method of optimization the stress state of an elastic beam, subjected to the simultaneous action of the central application of concentrated force and bending moment. Optimization method based on solving the inverse problem of the theory of elasticity of inhomogeneous bodies, the essence of which is to determine the law of changing the modulus of elasticity on the beams height for which stress state will be given.

scholarly journals A COMPLEMENTARY ENERGY THEOREM FOR COMPOSITE PLATES IN POSTBUCKLING

2019 ◽  
Author(s):  
Sergey Selyugin
Keyword(s):  
Stress State ◽  
Boundary Conditions ◽  
Stress Tensor ◽  
Composite Plates ◽  
Actual State ◽  
Complementary Energy ◽  
Displacement Gradient ◽  
Gradient Tensor ◽  
Internal Forces ◽  
Actual Stress

A composite von Karman plate in postbuckling is considered. Using the first Piola stress tensor and the displacement gradient tensor, a complementary energy variational theorem is proven. The proof is given in the case of symmetric lay-up. According to the theorem, at the actual stress state of the plate the complementary energy (as a function of the internal forces and of the moments) reaches its stationary value. The stationary feature of the actual state is valid as compared to other states satisfying the static equilibrium and the static boundary conditions. It is shown how the theorem may be generalized to the case of a non-symmetric lay-up.

scholarly journals Unilateral Contact of Elastic Bodies (Moment Theory)

2001 ◽  
Vol 8 (4) ◽  
pp. 753-766
Author(s):  
R. Gachechiladze
Keyword(s):  
Contact Zone ◽  
Couple Stress Theory ◽  
Contact Problems ◽  
Theory Of Elasticity ◽  
Unilateral Contact ◽  
Stress Theory ◽  
Nonhomogeneous Media ◽  
Elastic Bodies ◽  
The Moment ◽  
Boundary Contact

Abstract Boundary contact problems of statics of the moment (couple-stress) theory of elasticity are studied in the case of a unilateral contact of two elastic anisotropic nonhomogeneous media. A problem, in which during deformation the contact zone lies within the boundaries of some domain, and a problem, in which the contact zone can extend, are given a separate treatment. Concrete problems suitable for numerical realizations are considered.

Advanced Mechanics of Solids

2021 ◽  
Author(s):  
Lester W. Schmerr Jr.
Keyword(s):  
Undergraduate Students ◽  
Three Dimensional ◽  
Theory Of Elasticity ◽  
Mechanics Of Solids ◽  
Stress Strain ◽  
Elastic Bodies ◽  
Mechanics Of Materials ◽  
Modern Textbook ◽  
Elementary Mechanics ◽  
Matrix Vector

Build on the foundations of elementary mechanics of materials texts with this modern textbook that covers the analysis of stresses and strains in elastic bodies. Discover how all analyses of stress and strain are based on the four pillars of equilibrium, compatibility, stress-strain relations, and boundary conditions. These four principles are discussed and provide a bridge between elementary analyses and more detailed treatments with the theory of elasticity. Using MATLAB® extensively throughout, the author considers three-dimensional stress, strain and stress-strain relations in detail with matrix-vector relations. Based on classroom-proven material, this valuable resource provides a unified approach useful for advanced undergraduate students and graduate students, practicing engineers, and researchers.

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