scholarly journals Some Problems of Thermoelastic Equilibrium of a Rectangular Parallelepiped in Terms of Asymmetric Elasticity

2001 ◽  
Vol 8 (4) ◽  
pp. 767-784
Author(s):  
N. Khomasuridze
Keyword(s):  
Thermal Field ◽  
Separation Of Variables ◽  
Contact Problems ◽  
Rectangular Parallelepiped ◽  
Effective Solution ◽  
Contact Conditions ◽  
Thermoelastic Equilibrium ◽  
Boundary Contact ◽  
Asymmetric Elasticity ◽  
Surface Disturbances

Abstract An effective solution of a number of boundary value and boundary contact problems of thermoelastic equilibrium is constructed for a homogeneous isotropic rectangular parallelepiped in terms of asymmetric and pseudo-asymmetric elasticity (Cosserat's continuum and pseudo- continuum). Two opposite faces of a parallelepiped are affected by arbitrary surface disturbances and a stationary thermal field, while for the four remaining faces symmetry or anti-symmetry conditions (for a multilayer rectangular parallelepiped nonhomogeneous contact conditions are also defined) are given. The solutions are constructed in trigonometric series using the method of separation of variables.

Thermoelastic Equilibrium of Bodies in Generalized Cylindrical Coordinates

1998 ◽  
Vol 5 (6) ◽  
pp. 521-544
Author(s):  
N. Khomasuridze
Keyword(s):  
Separation Of Variables ◽  
Contact Problems ◽  
The Body ◽  
Cylindrical Coordinates ◽  
Thermoelastic Equilibrium ◽  
Transversally Isotropic ◽  
Boundary Contact ◽  
Plane Of Isotropy ◽  
Surface Disturbances ◽  
Orthogonal Coordinates

Abstract Using the method of separation of variables, an exact solution is constructed for some boundary value and boundary-contact problems of thermoelastic equilibrium of one- and multilayer bodies bounded by the coordinate surfaces of generalized cylindrical coordinates ρ, α, 𝑧. ρ, α are the orthogonal coordinates on the plane and 𝑧 is the linear coordinate. The body, occupying the domain Ω = {ρ 0 < ρ < ρ 1, α 0 < α < α 1, 0 < 𝑧 < 𝑧1}, is subjected to the action of a stationary thermal field and surface disturbances (such as stresses, displacements, or their combinations) for 𝑧 = 0 and 𝑧 = 𝑧1. Special type homogeneous conditions are given on the remainder of the surface. The elastic body is assumed to be transversally isotropic with the plane of isotropy 𝑧 = const and nonhomogeneous along 𝑧. The same assumption is made for the layers of the multilayer body which contact along 𝑧 = const.

Thermoelastic Equilibrium of A Rectangular Parallelepiped with Nonhomogeneous Symmetry and Antisymmetry Conditions on its Faces

2000 ◽  
Vol 7 (4) ◽  
pp. 701-722 ◽  
Author(s):  
N. Khomasuridze
Keyword(s):  
Exact Solution ◽  
Thermal Field ◽  
Displacement Vector ◽  
Separation Of Variables ◽  
Normal Component ◽  
Rectangular Parallelepiped ◽  
Thermoelastic Equilibrium ◽  
Tangential Stresses ◽  
In Series ◽  
Surface Disturbances

Abstract An exact solution of the boundary value problems of thermoelastic equilibrium of a homogeneous isotropic rectangular parallelepiped is constructed. The parallelepiped is affected by a stationary thermal field and surface disturbances, in particular, on each side of the rectangular parallelepiped the following parameters are defined: a normal component of the displacement vector and tangential stresses (nonhomogeneous symmetry conditions) or normal stress and tangential stresses (nonhomogeneous antisymmetry conditions). The solution of the problems is constructed in series using the method of separation of variables.

scholarly journals Solution of Contact Problems for Nonlinear Gao Beam and Obstacle

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
J. Machalová ◽  
H. Netuka
Keyword(s):  
Solution Method ◽  
Mixed Finite Element ◽  
Mixed Finite Element Method ◽  
Contact Problems ◽  
Beam Model ◽  
Contact Conditions ◽  
Beam Elements ◽  
Solution Methods ◽  
Euler Bernoulli Beam ◽  
Bernoulli Beam Model

Contact problem for a large deformed beam with an elastic obstacle is formulated, analyzed, and numerically solved. The beam model is governed by a nonlinear fourth-order differential equation developed by Gao, while the obstacle is considered as the elastic foundation of Winkler’s type in some distance under the beam. The problem is static without a friction and modeled either using Signorini conditions or by means of normal compliance contact conditions. The problems are then reformulated as optimal control problems which is useful both for theoretical aspects and for solution methods. Discretization is based on using the mixed finite element method with independent discretization and interpolations for foundation and beam elements. Numerical examples demonstrate usefulness of the presented solution method. Results for the nonlinear Gao beam are compared with results for the classical Euler-Bernoulli beam model.

Numerical Investigation on the Structural Behavior of a Composite Impact Absorber

2009 ◽  
Vol 417-418 ◽  
pp. 685-688 ◽  
Author(s):  
Giuseppe Lamanna ◽  
Francesco Caputo ◽  
Alessandro Soprano
Keyword(s):  
Numerical Investigation ◽  
Laminated Composite ◽  
Failure Criteria ◽  
Point Of View ◽  
Physical Parameters ◽  
Contact Conditions ◽  
Explicit Finite Element ◽  
Energy Absorbing ◽  
Boundary Contact ◽  
Composite Face

The energy absorption capability of an exposed crashworthy element or system is largely affected by material properties and structural design: prismatic sandwich structures, made of foam or honeycomb core between two metallic or laminated composite face plates, are good candidates. This work deals with a numerical investigation on the energy absorbing capability of such a structural component. There are several difficulties associated with the numerical simulation of a composite impact-absorber, such as high geometrical non-linearities, boundary contact conditions, failure criteria, material behaviour; that is because the main objectives of any numerical investigation are the calibration of the model with experimental results and the evaluation of the sensitivity of the variables with respect to the geometrical and physical parameters which influence the study at hand. The latter is a very relevant aspect for designers if the application of the model to real cases has to be a robust one from both a physical and a numerical point of view. In this paper a preliminary calibration of a numerical model for a composite impact absorber is presented, on the basis of experimental data found in literature; then a sensitivity analysis of the same model to the variation of the main geometrical and material parameters, developed by using the explicit finite element algorithms implemented in the Ls-Dyna code, is illustrated.

scholarly journals Boundary-contact problems for domains with conical singularities

2005 ◽  
Vol 217 (2) ◽  
pp. 456-500 ◽  
Author(s):  
David Kapanadze ◽  
B.-Wolfgang Schulze
Keyword(s):  
Contact Problems ◽  
Conical Singularities ◽  
Boundary Contact

scholarly journals Studies on Static Frictional Contact Problems of Double Cantilever Beam Based on SBFEM

2017 ◽  
Vol 11 (1) ◽  
pp. 896-905
Author(s):  
Zhu Chaolei ◽  
Gao Qian ◽  
Hu Zhiqiang ◽  
Lin Gao ◽  
Lu Jingzhou
Keyword(s):  
Mathematical Programming ◽  
Differential Equations ◽  
Cantilever Beam ◽  
Frictional Contact ◽  
Double Cantilever Beam ◽  
Contact Problems ◽  
Contact Forces ◽  
Contact Conditions ◽  
Good Convergence ◽  
Practical Engineering

Introduction: The frictional contact problem is one of the most important and challenging topics in solids mechanics, and often encountered in the practical engineering. Method: The nonlinearity and non-smooth properties result in that the convergent solutions can't be obtained by the widely used trial-error iteration method. Mathematical Programming which has good convergence properties and rigorous mathematical foundation is an effective alternative solution method, in which, the frictional contact conditions can be expressed as Non-smooth Equations, B-differential equations, Nonlinear Complementary Problem, etc. Result: In this paper, static frictional contact problems of double cantilever beam are analyzed by Mathematical Programming in the framework of Scaled Boundary Finite Element Method (SBFEM), in which the contact conditions can be expressed as the B-differential Equations. Conclusion The contact forces and the deformation with different friction factors are solved and compared with those obtained by ANSYS, by which the accuracy of solving contact problems by SBFEM and B-differential Equations is validated.

Modeling Compliant Part Assembly: Mechanics of Deformation and Contact

2000 ◽  
Author(s):  
Raju Mattikalli ◽  
Saba Mahanian ◽  
Alan Jones ◽  
Greg Clark
Keyword(s):  
Finite Element ◽  
Quadratic Programming ◽  
Variational Inequalities ◽  
Lagrange Multipliers ◽  
Contact Problems ◽  
Point Of View ◽  
Contact Conditions ◽  
Compliant Part ◽  
Variational Approaches ◽  
Compliant Parts

Abstract This paper describes an approach to model the mechanics of assembly by assuming parts are compliant. The approach involves a model of contact between compliant bodies based on variational inequalities. This approach has a number of advantages over current finite element codes, which rely on traditional variational approaches such as penalty force methods and Lagrange multipliers to resolve multiple unknown contact conditions. From a mathematical point of view, contact problems among compliant parts are particularly difficult to handle due to the fact that contact constraints are not permanently active, but depend on deformations. They are inherently non-linear and irreversible in character. To obtain a more mathematically robust way of modeling contact, we present a variational inequalities based approach that produces a quadratic programming (QP) problem. The QP is solved to resolve contact situations and obtain the mechanics of parts during assembly. We apply the method to simulate and design aircraft assembly processes.

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