General Stability Analysis of Lattice Shells by Continuum Modeling

1992 ◽  
Vol 7 (4) ◽  
pp. 275-283 ◽  
Author(s):  
Jozef Sumec
Keyword(s):  
Elastic Stability ◽  
Analytical Form ◽  
Continuum Modeling ◽  
Shallow Shells ◽  
Linear Elastic ◽  
Analytical Expressions ◽  
Point Of Departure ◽  
Theoretical Results ◽  
Lattice Shells ◽  
The Continuum

In this paper a linear elastic stability problem of lightweight lattice shells is studied. For this purpose a calculation on an equivalent rigidity continuum model is used. It is assumed that the rods of the analysed shells consist of a homogeneous, isotropic elastic material the mechanical properties of which are invariant in the time. The Author derived analytical expressions the point of departure of which is the theory of finite deflections of shallow shells. The use of the Bubnov-Galerkine method allows to define a relationships yielding the values of critical stress in closed analytical form. The effect of initial geometrical shell imperfections of the “medial” surface is taken into consideration, too. Sample numerical results are presented to demonstrate the effectiveness of the continuum modeling approach. The obtained theoretical results are documented some of the numerical examples.

scholarly journals Continuum modeling perspectives of non-Fourier heat conduction in biological systems

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Ákos Sudár ◽  
Gergely Futaki ◽  
Róbert Kovács
Keyword(s):  
Biological Systems ◽  
Phase Lag ◽  
Dual Phase ◽  
Continuum Modeling ◽  
Biological Origin ◽  
Ultrasound Surgery ◽  
Thermal Models ◽  
Wide Range ◽  
Fourier Heat Conduction ◽  
The Continuum

Abstract The thermal modeling of biological systems is increasingly important in the development of more advanced and more precise techniques such as ultrasound surgery. One of the primary barriers is the complexity of biological materials: the geometrical, structural, and material properties vary in a wide range. In the present paper, we focus on the continuum modeling of heterogeneous materials of biological origin. There are numerous examples in the literature for non-Fourier thermal models. However, as we realized, they are associated with a few common misconceptions. Therefore, we first aim to clarify the basic concepts of non-Fourier thermal models. These concepts are demonstrated by revisiting two experiments from the literature in which the Cattaneo–Vernotte and the dual phase lag models are utilized. Our investigation revealed that these non-Fourier models are based on misinterpretations of the measured data, and the seeming deviation from Fourier’s law originates from the source terms and boundary conditions.

Linear and non-linear elastic stability of beams by higher order beam theories

2019 ◽  
Author(s):  
Αμαλία Αργυρίδη
Keyword(s):  
Elastic Stability ◽  
Higher Order ◽  
Linear Elastic ◽  
Non Linear ◽  
Fortran 90 ◽  
Beam Theories

Στην παρούσα διδακτορική διατριβή διερευνάται η γραμμική και μη γραμμική ελαστική ευστάθεια ράβδων διαμέσου θεωριών δοκού ανώτερης τάξης. Προκειμένου να υλοποιηθεί αυτό, το πρώτο βήμα της παρούσας διδακτορικής διατριβής είναι η εξέταση του στρεπτοκαμπτικού λυγισμού σύμμικτων δοκών λαμβάνοντας υπόψη τα φαινόμενα της στρέβλωσης (εκτός επιπέδου παραμόρφωση) και την διατμητικής υστέρησης (διαφοροποίηση της κλασσικής κατανομής ορθών τάσεων) λόγω κάμψης και στρέψης. Στο δεύτερο βήμα της παρούσας διδακτορικής διατριβής, μορφώνεται το πρόβλημα της γραμμικής κα μη γραμμικής στατικής ανάλυσης ομογενών δοκών λαμβάνοντας υπόψη τα φαινόμενα της αξονικής στρέβλωσης και της διαστρέβλωσης (εντός επιπέδου παραμόρφωση) επιπρόσθετα σε εκείνα λόγω της καμπτικής και στρεπτικής συμπεριφοράς της δοκού διαμέσου του σχήματος διαδοχικής ισορροπίας που υιοθετείται (πλεονεκτήματα έναντι προβλημάτων ιδιοτιμών). Κύριο τμήμα του δεύτερου βήματος αποτελεί η διατύπωση, η αρχικοποίηση και η επίλυση των προβλημάτων συνοριακών τιμών που αφορούν στον υπολογισμό των αξονικών μορφών στρέβλωσης και διαστρέβλωσης διαμέσου του σχήματος διαδοχικής ισορροπίας. Στο προτελευταίο βήμα της παρούσας διδακτορικής διατριβής, οι προηγούμενα αναπτυγμένες αξονικές μορφές στρέβλωσης και διαστρέβλωσης μαζί με τις αντίστοιχες καμπτικές και στρεπτικές χρησιμοποιούνται προκειμένου να μορφωθεί και να επιλυθεί το πρόβλημα της γραμμικής ελαστικής ευστάθειας δοκών. Στο τελευταίο βήμα της παρούσας διδακτορικής διατριβής, διεξάγεται μη γραμμική ανάλυση λαμβάνοντας υπόψη τα φαινόμενα της στρέβλωσης και της διαστρέβλωσης λόγω αξονικής, διατμητικής, καμπτικής και στρεπτικής δομικής συμπεριφοράς και πραγματοποιείται σύγκριση με τα αντίστοιχα αποτελέσματα που λαμβάνονται στην περίπτωση όπου λαμβάνεται υπόψη μόνο η στρέβλωση και η διατμητική υστέρηση λόγω κάμψης και στρέψης. Αξίζει να σημειωθεί ότι σε όλες τις παραπάνω περιπτώσεις η διατομή της δοκού είναι τυχούσα, ενώ ο λόγος του Poisson λαμβάνεται υπόψη στον υπολογισμό των αξονικών, καμπτικών και στρεπτικών μορφών στρέβλωσης και διαστρέβλωσης. Στην παρούσα διδακτορική διατριβή χρησιμοποιούνται δύο αριθμητικές μέθοδοι. Η πρώτη είναι η μέθοδος των συνοριακών στοιχείων που χρησιμοποιείται για την επίλυση των προβλημάτων συνοριακών τιμών που αφορούν στον υπολογισμό των αξονικών, καμπτικών και στρεπτικών μορφών στρέβλωσης και διαστρέβλωσης και των γεωμετρικών σταθερών. Η δεύτερη μέθοδος είναι η μέθοδος των πεπερασμένων στοιχείων που χρησιμοποιείται για τη διακριτοποίηση των και την επίλυση των καθολικών εξισώσεων ισορροπίας της δοκού. Στη βάση των αναλυτικών και αριθμητικών μεθόδων που παρουσιάζονται στην παρούσα διδακτορική διατριβή έχουν γραφτεί προγράμματα σε FORTRAN 90/95 και έχουν μελετηθεί αντιπροσωπευτικά αριθμητικά παραδείγματα. Επιπρόσθετα, έχουν γραφτεί scripts σε MATLAB προκειμένου να ερμηνευθούν τα αποτελέσματα διαμέσου δισδιάστατων και τρισδιάστατων γραφημάτων της δοκού. Η ακρίβεια και η αξιοπιστία των προτεινόμενων μεθόδων επιβεβαιώνονται μέσω αριθμητικών παραδειγμάτων που αντλούνται από τη βιβλιογραφία και αποτελεσμάτων που εξάγονται από αναλύσεις τρισδιάστατων και επιφανειακών πεπερασμένων στοιχείων.

STUDY OF THERMODYNAMIC PROPERTIES OF ZINC-BLENDE-TYPE SEMICONDUCTORS: TEMPERATURE AND PRESSURE DEPENDENCES

2011 ◽  
Vol 25 (12n13) ◽  
pp. 1041-1051 ◽  
Author(s):  
HO KHAC HIEU ◽  
VU VAN HUNG
Keyword(s):  
Nearest Neighbor ◽  
Thermodynamic Quantities ◽  
Atomic Displacements ◽  
Zinc Blende ◽  
The Mean ◽  
Temperature And Pressure ◽  
Analytical Expressions ◽  
Theoretical Results ◽  
Nearest Neighbor Distances ◽  
Statistical Moment Method

Using the statistical moment method (SMM), the temperature and pressure dependences of thermodynamic quantities of zinc-blende-type semiconductors have been investigated. The analytical expressions of the nearest-neighbor distances, the change of volumes and the mean-square atomic displacements (MSDs) have been derived. Numerical calculations have been performed for a series of zinc-blende-type semiconductors: GaAs , GaP , GaSb , InAs , InP and InSb . The agreement between our calculations and both earlier other theoretical results and experimental data is a support for our new theory in investigating the temperature and pressure dependences of thermodynamic quantities of semiconductors.

scholarly journals Non-linear analysis of laminated composite doubly curved shallow shells

2006 ◽  
Vol 28 (1) ◽  
pp. 43-55
Author(s):  
Dao Huy Bich
Keyword(s):  
Laminated Composite ◽  
Governing Equations ◽  
Shallow Shells ◽  
Approximate Analytical Solutions ◽  
Linear Buckling ◽  
Non Linear ◽  
Vibration Problems ◽  
Doubly Curved ◽  
Analytical Expressions ◽  
Load Deflection Curve

This paper deals with governing equations and approximate analytical solutions based on some wellknown assumptions to the non-linear buckling and vibration problems of laminated composite doubly curved shallow shells. Obtained results will be presented by analytical expressions of the lower critical load, the postbuckling load-deflection curve and the fundamental frequency of non-linear free vibration of the shell.

Shakedown in Frictional Contact Problems

2007 ◽  
Author(s):  
J. R. Barber ◽  
A. Klarbring ◽  
M. Ciavarella
Keyword(s):  
Frictional Contact ◽  
Elastic System ◽  
Contact Problems ◽  
Sufficient Condition ◽  
Normal Contact ◽  
Linear Elastic ◽  
Periodic Loading ◽  
Continuum Formulation ◽  
Complete Contact ◽  
The Continuum

If a linear elastic system with frictional interfaces is subjected to periodic loading, any slip which occurs generally reduces the tendency to slip during subsequent cycles and in some circumstances the system ‘shakes down’ to a state without slip. It has often been conjectured that a frictional Melan’s theorem should apply to this problem — i.e. that the existence of a state of residual stress sufficient to prevent further slip is a sufficient condition for the system to shake down. Here we discuss recent proofs that this is indeed the case for ‘complete’ contact problems if there is no coupling between relative tangential displacements at the interface and the corresponding normal contact tractions. By contrast, when coupling is present, the theorem applies only for a few special two-dimensional discrete cases. Counter-examples can be generated for all other cases. These results apply both in the discrete and the continuum formulation.

scholarly journals A Review of Geometry, Construction and Modelling for Carbon Nanotori

2019 ◽  
Vol 9 (11) ◽  
pp. 2301 ◽  
Author(s):  
Pakhapoom Sarapat ◽  
James Hill ◽  
Duangkamon Baowan
Keyword(s):  
Carbon Nanotubes ◽  
Carbon Nanostructures ◽  
Single Walled Carbon Nanotubes ◽  
Continuum Approximation ◽  
Interaction Energies ◽  
Jones Potential ◽  
Lennard Jones ◽  
Walled Carbon Nanotubes ◽  
Analytical Expressions ◽  
The Continuum

After the discovery of circular formations of single walled carbon nanotubes called fullerene crop circles, their structure has become one of the most researched amongst carbon nanostructures due to their particular interesting physical properties. Several experiments and simulations have been conducted to understand these intriguing objects, including their formation and their hidden characteristics. It is scientifically conceivable that these crop circles, nowadays referred to as carbon nanotori, can be formed by experimentally bending carbon nanotubes into ring shaped structures or by connecting several sections of carbon nanotubes. Toroidal carbon nanotubes are likely to have many applications, especially in electricity and magnetism. In this review, geometry, construction, modelling and possible applications are discussed and the existing known analytical expressions, as obtained from the Lennard-Jones potential and the continuum approximation, for their interaction energies with other nanostructures are summarised.

Bending of lightweight circular tubes

2017 ◽  
Vol 232 (7) ◽  
pp. 1165-1178 ◽  
Author(s):  
G Mastinu ◽  
G Previati ◽  
M Gobbi
Keyword(s):  
Lightweight Design ◽  
Analytical Form ◽  
Upper And Lower Bounds ◽  
Concept Design ◽  
Optimal Solutions ◽  
Lightweight Construction ◽  
Linear Elastic ◽  
Design Variables ◽  
Maximum Stiffness ◽  
Linear Elastic Theory

The concept design (sizing) of thin-walled tubes subject to bending is dealt by resorting to rigorous design principles pertaining to engineering science. Multi-objective optimization is the proper theory that has been exploited. Minimum mass and maximum stiffness (minimum compliance) are the optimization objectives. Safety (admissible stress), stability (buckling), available room (external radius of the tube), and thickness of the tube (arising from technological issues) are introduced as constraints. Linear elastic theory is used. Optimal solutions are given in analytical form for a prompt use by designers. Such optimal solutions refer both to the objectives (mass and compliance) and to the design variables (radius and thickness of the tube). The best attainable lightweight design is discussed as a function of the constraints. In particular, given the upper and lower bounds for radius and thickness respectively, three candidate optimal solutions are addressed in the paper for concept design purposes. The comparative lightweight design of tubes made from different materials is presented. Contrary with respect to the reputation of aluminum for effective lightweight construction, steel can be the best choice, when the available room has to be saturated.

scholarly journals Tensor pomeron, vector odderon and diffractive production of meson and baryon pairs in proton-proton collisions

2019 ◽  
Vol 206 ◽  
pp. 06005 ◽  
Author(s):  
Piotr Lebiedowicz ◽  
Otto Nachtmann ◽  
Antoni Szczurek
Keyword(s):  
Experimental Data ◽  
High Energy ◽  
Proton Proton ◽  
Proton Collisions ◽  
High Energies ◽  
Energy Proton ◽  
Diffractive Production ◽  
Proton Proton Collisions ◽  
Theoretical Results ◽  
The Continuum

We review some selected results of the tensor-pomeron and vectorodderon model of soft high-energy proton-proton scattering and central exclusive production of meson and baryon pairs in proton-proton collisions. We discuss the theoretical aspects of this approach and consider the phenomenological implications in a variety of processes at high energies, comparing to existing experimental data. We consider the diffractive dipion and dikaon production including the continuum and the dominant scalar and tensor resonance contributions as well as the photoproduction processes. The theoretical results are compared with existing CDF experimental data and predictions for planned or current LHC experiments, ALICE, ATLAS, CMS, LHCb are presented.

A study on the linear elastic stability of Mindlin plates

1986 ◽  
Vol 22 (1) ◽  
pp. 117-132 ◽  
Author(s):  
Y. K. Cheung ◽  
A. H. C. Chan ◽  
L. G. Tham
Keyword(s):  
Elastic Stability ◽  
Linear Elastic
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