scholarly journals Formulation of the pextension finite elements for the solution of normal contact problems

2020 ◽  
Vol 15 (2) ◽  
pp. 135-172
Author(s):  
István Páczelt ◽  
Attila Baksa ◽  
Tamás Szabó
Keyword(s):  
Finite Elements ◽  
High Efficiency ◽  
Contact Problems ◽  
Solution Procedure ◽  
Fixed Number ◽  
Minimum Potential Energy ◽  
Normal Contact ◽  
Minimum Potential ◽  
Contact Domain ◽  
Small Elements

This work deals with normal contact problems. After a wide literature review, we look for the possibility of achieving a high-precision solution using the principle of minimum potential energy and the Hellinger-Reissner variational principle with penalty and augmented Lagrangian techniques. By positioning of the border of the contact elements, the whole surfaces of the eligible elements fall in contact or in gap regions. This reduces the error of the singularity in the border of the contact domain. Computations with $h$-, $p$- and $rp$-versions are performed. For the $rp$-version, the pre-fixed number of finite elements are moved so that small elements are placed in one or two element layers at the ends of the contact zone. A number of diagrams and tables showing the convergence of the solution (by increasing the number of polynomial degrees p) demonstrate the high efficiency of the proposed solution procedure.

scholarly journals Viscoelastic Effects during Tangential Contact Analyzed by a Novel Finite Element Approach with Embedded Interface Profiles

Lubricants ◽  
2020 ◽  
Vol 8 (12) ◽  
pp. 107
Author(s):  
Jacopo Bonari ◽  
Marco Paggi
Keyword(s):  
Finite Elements ◽  
Contact Problem ◽  
Finite Thickness ◽  
Viscoelastic Model ◽  
Contact Problems ◽  
Partial Slip ◽  
Viscoelastic Layer ◽  
Model Approximation ◽  
Normal Contact ◽  
Viscoelastic Effects

A computational approach that is based on interface finite elements with eMbedded Profiles for Joint Roughness (MPJR) is exploited in order to study the viscoelastic contact problems with any complex shape of the indenting profiles. The MPJR finite elements, previously developed for partial slip contact problems, are herein further generalized in order to deal with finite sliding displacements. The approach is applied to a case study concerning a periodic contact problem between a sinusoidal profile and a viscoelastic layer of finite thickness. In particular, the effect of using three different rheological models that are based on Prony series (with one, two, or three arms) to approximate the viscoelastic behaviour of a real polymer is investigated. The method allows for predicting the whole transient regime during the normal contact problem and the subsequent sliding scenario from full stick to full slip, and then up to gross sliding. The effects of the viscoelastic model approximation and of the sliding velocities are carefully investigated. The proposed approach aims at tackling a class of problems that are difficult to address with other methods, which include the possibility of analysing indenters of generic profile, the capability of simulating partial slip and gross slip due to finite slidings, and, finally, the possibility of simultaneously investigating dissipative phenomena, like viscoelastic dissipation and energy losses due to interface friction.

scholarly journals Staircase Quantum Dots Configuration in Nanowires for Optimized Thermoelectric Power

2016 ◽  
Vol 6 (1) ◽  
Author(s):  
Lijie Li ◽  
Jian-Hua Jiang
Keyword(s):  
Quantum Dots ◽  
Output Power ◽  
High Efficiency ◽  
Fixed Number ◽  
Transport Processes ◽  
Thermoelectric Device ◽  
Single Pair ◽  
Thermoelectric Devices ◽  
Serial Connection ◽  
Inelastic Transport

Abstract The performance of thermoelectric energy harvesters can be improved by nanostructures that exploit inelastic transport processes. One prototype is the three-terminal hopping thermoelectric device where electron hopping between quantum-dots are driven by hot phonons. Such three-terminal hopping thermoelectric devices have potential in achieving high efficiency or power via inelastic transport and without relying on heavy-elements or toxic compounds. We show in this work how output power of the device can be optimized via tuning the number and energy configuration of the quantum-dots embedded in parallel nanowires. We find that the staircase energy configuration with constant energy-step can improve the power factor over a serial connection of a single pair of quantum-dots. Moreover, for a fixed energy-step, there is an optimal length for the nanowire. Similarly for a fixed number of quantum-dots there is an optimal energy-step for the output power. Our results are important for future developments of high-performance nanostructured thermoelectric devices.

Interaction Model for “Shelled Particles” and Small-Strain Modulus of Granular Materials

2018 ◽  
Vol 85 (10) ◽  
Author(s):  
Shun-hua Zhou ◽  
Peijun Guo ◽  
Dieter F. E. Stolle
Keyword(s):  
Elastic Modulus ◽  
Contact Stiffness ◽  
Scaling Law ◽  
Interaction Model ◽  
Contact Problems ◽  
Hertzian Contact ◽  
Spherical Particles ◽  
Thin Coating ◽  
Normal Contact ◽  
Laboratory Test Results

The elastic modulus of a granular assembly composed of spherical particles in Hertzian contact usually has a scaling law with the mean effective pressure p as K∼G∼p1/3. Laboratory test results, however, reveal that the value of the exponent is generally around 1/2 for most sands and gravels, but it is much higher for reclaimed asphalt concrete composed of particles coated by a thin layer of asphalt binder and even approaching unity for aggregates consisting of crushed stone. By assuming that a particle is coated with a thin soft deteriorated layer, an energy-based simple approach is proposed for thin-coating contact problems. Based on the features of the surface layer, the normal contact stiffness between two spheres varies with the contact force following kn∼Fnm and m∈[1/3,  1], with m=1/3 for Hertzian contact, m=1/2 soft thin-coating contact, m=2/3 for incompressible soft thin-coating, and m=1 for spheres with rough surfaces. Correspondingly, the elastic modulus of a random granular packing is proportional to pm with m∈[1/3,  1].

Principles of minimum potential energy and complementary energy

2020 ◽  
pp. 228-248
Author(s):  
Lallit Anand ◽  
Sanjay Govindjee
Keyword(s):  
Boundary Condition ◽  
Potential Energy ◽  
Displacement Field ◽  
Mixed Boundary ◽  
Energy Functional ◽  
The Body ◽  
Minimum Potential Energy ◽  
Complementary Energy ◽  
Minimum Potential ◽  
Potential Energy Functional

With the displacement field taken as the only fundamental unknown field in a mixed-boundary-value problem for linear elastostatics, the principle of minimum potential energy asserts that a potential energy functional, which is defined as the difference between the free energy of the body and the work done by the prescribed surface tractions and the body forces --- assumes a smaller value for the actual solution of the mixed problem than for any other kinematically admissible displacement field which satisfies the displacement boundary condition. This principle provides a weak or variational method for solving mixed boundary-value-problems of elastostatics. In particular, instead of solving the governing Navier form of the partial differential equations of equilibrium, one can search for a displacement field such that the first variation of the potential energy functional vanishes. A similar principle of minimum complementary energy, which is phrased in terms of statically admissible stress fields which satisfy the equilibrium equation and the traction boundary condition, is also discussed. The principles of minimum potential energy and minimum complementary energy can also be applied to derive specialized principles which are particularly well-suited to solving structural problems; in this context the celebrated theorems of Castigliano are discussed.

Optimization for Minimum Potential Energy, Maximum Rigidity and Minimum Deformability

1984 ◽  
pp. 9-87
Author(s):  
Andrej M. Brandt ◽  
Wojciech Dzieniszewski ◽  
Stefan Jendo ◽  
Wojciech Marks ◽  
Stefan Owczarek ◽  
...  
Keyword(s):  
Potential Energy ◽  
Minimum Potential Energy ◽  
Minimum Potential ◽  
Energy Maximum

A Global Extremum Principle in Mixed Form for Equilibrium Analysis With Elastic/Stiffening Materials (a Generalized Minimum Potential Energy Principle)

1994 ◽  
Vol 61 (4) ◽  
pp. 914-918 ◽  
Author(s):  
J. E. Taylor
Keyword(s):  
Potential Energy ◽  
Problem Formulation ◽  
Extremum Problem ◽  
Equilibrium Analysis ◽  
Minimum Potential Energy ◽  
Problem Statement ◽  
Energy Principle ◽  
Potential Energy Principle ◽  
Minimum Potential ◽  
Minimum Potential Energy Principle

An extremum problem formulation is presented for the equilibrium mechanics of continuum systems made of a generalized form of elastic/stiffening material. Properties of the material are represented via a series composition of elastic/locking constituents. This construction provides a means to incorporate a general model for nonlinear composites of stiffening type into a convex problem statement for the global equilibrium analysis. The problem statement is expressed in mixed “stress and deformation” form. Narrower statements such as the classical minimum potential energy principle, and the earlier (Prager) model for elastic/locking material are imbedded within the general formulation. An extremum problem formulation in mixed form for linearly elastic structures is available as a special case as well.

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