ĈҤI HӐC QUӔC GIA TP. HӖ &+Ë0,1+
75ѬӠ1*ĈҤI HӐ&%È&+.+2$
--------------------
TRҪN QUANG SӺ
3+Æ17Ë&+ӬNG XӰ ĈӜNG CӪA TҨM FGM CHӎU
TҦI TRӐNG DI CHUYӆ1 &Ï;e7ĈӂN Ҧ1++ѬӢNG
CӪA NHIӊ7ĈӜ SӰ DӨ1*3+ѬѪ1* 3+È3
PHҪN TӰ CHUYӆ1 ĈӜNG - MEM
&KX\rQQJjQK Kӻ thuұW[k\Gӵng
0mVӕ: 8580201
LUҰ19Ă17+Ҥ&6Ƭ
TP. HӖ &+Ë0,1+WKiQJQăP
&Ð1* 75Î1+ ĈѬӦ& +2¬1 7+¬1+ 7ҤI:
75ѬӠ1* ĈҤI HӐ& %È&+ .+2$
ĈҤI HӐC QUӔC GIA TP. HӖ &+Ë0,1+
&iQEӝ hѭӟng dүn khoa hӑc: TS. Trҫn Minh Thi
&iQbӝ chҩm nhұQ[pW TS. NguyӉQ3K~&ѭӡng
&iQEӝ chҩm nhұQ[pW TS. NguyӉn TҩQ&ѭӡng
Luұn văn thҥFVƭÿѭӧc bҧo vӋ tҥL7UѭӡQJĈҥi hӑF%iFK.KRDĈ+4* 7S+&0
QJj\WKiQJQăm 2021 (trӵc tuyӃn).
7KjQKSKҫn HӝLÿӗQJÿiQKJLi/XұQYăQWKҥFVƭJӗm:
1. PGS.TS. Hӗ Ĉӭc Duy .................- Chӫ tӏch
3*676 &DR9ăQ9XL ................- 7KѭNê
3. TS. Trҫn Minh Thi........................- Ӫ\YLrQ
4. TS. NguyӉQ3K~&ѭӡng ...............- Phҧn biӋn 1
5. TS. NguyӉn TҩQ&ѭӡng ...............- Phҧn biӋn 2
CHӪ TӎCH HӜ,ĈӖNG
75ѬӢNG KHOA
KӺ THUҰ7 ;Æ< 'ӴNG
ĈҤI HӐC QUӔC GIA TP.HCM
CӜ1*+Ñ$;+ӜI CHӪ 1*+Ƭ$9,ӊT NAM
75ѬӠ1*ĈҤI HӐC %È&+.+2$
Ĉӝc Lұp - Tӵ Do - HҥQK3K~F
1+,ӊ0 9Ө/8Ұ1 9Ă1 7+Ҥ& 6Ƭ
Hӑ YjWrQKӑFYLrQ: TRҪN QUANG SӺ
MSHV: 1970467
1Jj\WKiQJQăm sinh: 10/02/1996
Nѫi sinh: QuҧQJ1JmL
&KX\rQQJjQK .ӻ thuұW[k\Gӵng
0mVӕ: 8580201
I. 7Ç1 Ĉӄ 7¬,: 3KkQ WtFKӭng xӱ ÿӝng cӫa tҩm FGM chӏu tҧi trӑng di chuyӇn
Fy[pWÿӃn ҧQKKѭӣng cӫa nhiӋWÿӝ sӱ dөQJSKѭѫQJ SKiSSKҫn tӱ chuyӇQÿӝng
± MEM.
II. NHIӊM VӨ 9¬ 1ӜI DUNG
1. ThiӃt lұSFiFPDWUұn khӕLOѭӧng, ma trұQÿӝ cӭQJYjPDWUұn cҧQFKRFiFSKҫn tӱ
kӃt cҩu tҩm FGM sӱ dөQJSKѭѫQJSKiSSKҫn tӱ chuyӇQÿӝng.
2. 3KiWWULӇn thuұWWRiQOұSWUuQKWtQKWRiQEҵQJFKѭѫQJWUuQK0DWODEÿӇ giҧi hӋ SKѭѫQJ
WUuQKÿӝng tәng thӇ cӫDEjLWRiQ
3. KiӇP WUDÿӝ tin cұy cӫDFKѭѫQJ WUuQKWtQKEҵQJFiFKVRViQKNӃt quҧ cӫDFKѭѫQJ
WUuQKYӟi kӃt quҧ FiFEjLEiRWKDPNKҧo.
4. TiӃQKjQKWKӵc hiӋQFiFYtGө sӕ nhҵm khҧRViWҧQKKѭӣng cӫDFiFQKkQWӕ quan
trӑQJÿӃn ӭng xӱ ÿӝng cӫa kӃt cҩu tҩm, tӯ ÿyU~WUDFiFNӃt luұQYjNLӃn nghӏ.
III. 1*¬< *,$2 1+,ӊM VӨ
: 22/02/2021
IV. 1*¬< +2¬1 7+¬1+ 1+,ӊM VӨ : 05/08/2021
V. HӐ 9¬ 7Ç1 &È1 %Ӝ HѬӞNG DҮN: TS. Trҫn Minh Thi
7S+&0 QJj\WKiQJQăm 2021
CHӪ NHIӊM BӜ 0Ð1
(Hӑ WrQYjFKӳ Nê
&È1 %Ӝ HѬӞNG DҮN
(Hӑ WrQYjFKӳ Nê
TS. TRҪN MINH THI
75ѬӢNG KHOA KӺ THUҰ7 ;Æ< 'ӴNG
(Hӑ WrQYjFKӳ Nê
i
/Ӡ,&Ҧ0 Ѫ1
/XұQYăQWKҥFVƭ;k\GӵQJF{QJWUuQKGkQGөQJYjF{QJQJKLӋSQҵPWURQJKӋWKӕQJ
EjLOXұQFXӕLNKyDQKҵPWUDQJEӏFKR+ӑFYLrQFDRKӑFNKҧQăQJ WӵQJKLrQFӭXELӃW
FiFKJLҧLTX\ӃWQKӳQJYҩQÿӅFөWKӇÿһWUDWURQJWKӵFWӃ[k\GӵQJĈyOjWUiFKQKLӋPYj
QLӅPWӵKjRFӫDPӛLKӑFYLrQFDRKӑF
ĈӇKRjQWKjQKOXұQYăQQj\QJRjLVӵFӕJҳQJ YjQӛOӵFFӫDEҧQWKkQW{Lÿm QKұQ
ÿѭӧFVӵJL~SÿӥQKLӅXWӯWұSWKӇYjFiFFiQKkQ7{L[LQJKLQKұQYjWӓOzQJELӃWѫQÿӃQ
WұSWKӇYjFiFFiQKkQÿmGjQKFKRW{LVӵJL~SÿӥTXêEiXÿy
ĈҫXWLrQW{L[LQEj\WӓOzQJELӃWѫQVkXVҳFÿӃQWKҫ\767UҫQ0LQK7KL7Kҫ\ÿmÿѭD
UDJӧL êÿҫXWLrQÿӇKuQKWKjQKQrQêWѭӣQJFӫDÿӅWjLYj7Kҫ\JySêFKRW{LUҩWQKLӅX
YӅFiFKQKұQÿӏQKÿ~QJÿҳQWURQJQKӳQJ YҩQÿӅQJKLrQFӭX FNJQJQKѭFiFKWLӃSFұQ
QJKLrQFӭXKLӋXTXҧ;LQFKkQWKjQKFҧPѫQWKҫ\76 &DR7ҩQ1JӑF7KkQÿmKӛWUӧ
JL~SÿӥWURQJTXiWuQKKӑFYLrQWKӵFKLӋQOXұQYăQ
7{L[LQFKkQWKjQKFҧPѫQTXê7Kҫ\&{.KRD.ӻ7KXұW;k\GӵQJWUѭӡQJĈҥLKӑF
%iFK.KRD- Ĉ+4* 7S+&0 ÿmWUX\ӅQGҥ\QKӳQJNLӃQWKӭFTXêJLiFKRW{LÿyFNJQJ
OjQKӳQJNLӃQWKӭFNK{QJWKӇWKLӃXWUrQFRQÿѭӡQJQJKLrQFӭXNKRDKӑF YjVӵQJKLӋS
FӫDW{LVDXQj\
/XұQYăQWKҥFVƭ ÿmKRjQWKjQKWURQJWKӡLJLDQ TX\ÿӏQKYӟLWuQKKuQKGӏFK&RYLG
FăQJWKҷQJEҵQJVӵQӛOӵFFӫDEҧQWKkQWX\QKLrQNK{QJWKӇNK{QJFyQKӳQJWKLӃXVyW
.tQKPRQJ TXê7Kҫ\&{ FKӍGүQWKrPÿӇW{LEәVXQJQKӳQJNL ӃQWKӭFYjKRjQWKLӋQ
EҧQWKkQPuQKKѫQ
;LQWUkQWUӑQJFҧPѫQ
7S+&0 QJj\WKiQJQăP
ii
7Ï0 7Ҳ7 /8Ұ1 9Ă1 7+Ҥ& 6Ƭ
&RPSRVLWHOjYұt liӋXÿѭӧc tәng hӧSQrQWӯ hai hay nhiӅu loҥi vұt liӋXNKiFQKDX
nhҵm mөFÿtFKWҥRQrQPӝt vұt liӋu mӟLѭXYLӋWYjEӅQKѫQVRYӟLFiFYұt liӋXEDQÿҫu.
Vұt liӋXFyFѫWtQKELӃQWKLrQKD\FzQJӑLOjYұt liӋu biӃQÿәi chӭFQăQJ )XQFWLRQaly
Graded Materials - )*0 OjPӝt loҥLFRPSRVLWHÿһc biӋWNK{QJÿӗng nhҩWÿҷQJKѭӟng
FyWtQKFKҩWFѫKӑFWKD\ÿәLOLrQWөc theo chiӅXGj\WҩPYjÿѭӧc sӱ dөng phә biӃn nhҩt
ÿӇ hoҥWÿӝQJWURQJP{LWUѭӡng nhiӋWÿӝ. Vұt liӋX)*0 ÿLӇQKuQKÿѭӧc tҥRWKjQKWӯ hai
WKjQKSKҫn: gӕP FHUDPLF YjNLPORҥL PHWDO 7KjQKSKҫn gӕm vӟLP{ ÿXQÿjQKӗi
FDRYjFiFKӋ sӕ JLmQQӣ nhiӋWYjWUX\Ӆn nhiӋt rҩt thҩSOjPFKRYұt liӋu chӭFQăQJFyÿӝ
cӭQJFDRYjUҩWWUѫYӟi nhiӋW7URQJNKLÿyWKjQKSKҫn kim loҥLOjPFKRYұt liӋu chӭc
QăQJFyWtQKGҿo dai, khҳc phөc sӵ rҥn nӭt nӃXFy[ҧ\UDGRWtQKGzQFӫa gӕPYjWURQJ
P{LWUѭӡng nhiӋWÿӝ cao. ѬXÿLӇm cӫa vұt liӋu chӭFQăQJÿyOjNKҧ QăQJFKӃ tҥRFiFNӃt
cҩu theo nhӳQJÿһFWtQKPRQJPXӕn cӫDQJѭӡi sӱ dөQJWURQJFiFÿLӅu kiӋQOjPYLӋc cө
thӇÿһc biӋWWURQJFiFP{LWUѭӡng cҫn chӏu nhiӋt, va chҥPPjLPzQ7URQJOƭQKYӵc
[k\GӵQJ EjLWRiQWҩPWUrQQӅn pasternak rҩWFyêQJKƭDYjFyWtQKӭng dөQJFDRQKѭ
nӅQPyQJFiFF{QJWUuQKGkQGөQJF{QJQJKLӋSJLDRWK{QJOzSKҧn ӭng,... Trong mӝt
khoҧng thӡi gian ngҳQÿmFyUҩt nhiӅu vҩQÿӅ OLrQTXDQÿӃQEjLWRiQSKkQWtFKNӃt cҩu
tҩP)*0 ÿѭӧFQJKLrQFӭXÿһc biӋWOjӭng xӱ cӫa tҩPWUrQQӅQÿjQQKӟt khi chӏu tҧi
trӑQJÿӝQJĈӇ SKkQWtFKÿӝng lӵc hӑFEjLWRiQWҩPWUrQQӅQSDVWHUQDNP{KuQKWҩm Yj
nӅQÿmÿѭӧFiSGөng. LuұQYăQQj\WұSWUXQJSKkQWtFKӭng xӱ ÿӝng cӫa kӃt cҩu tҩm
)*0 WKHRP{ KuQKWҩP Gj\5HLVVQHU-Mindlin sӱ dөQJSKѭѫQJ SKiSSKҫn tӱ chuyӇn
ÿӝQJ0(0 0RYLQJ(OHPHQW0HWKRG Fy[pWÿӃn ҧQKKѭӣng cӫa nhiӋWÿӝ&iFQJKLrQ
cӭXWUѭӟFÿk\WKѭӡng chӍ P{KuQKNӃt cҩu tҩm chӏu tҧLGLÿӝng sӱ dөQJSKѭѫQJSKiS
giҧLWtFKSKѭѫQJSKiSSKҫn tӱ hӳu hҥQ)(0 KD\SKѭѫQJ SKiSSKҫn tӱ chuyӇQÿӝng
0(0 QKѭQJFKѭD[pWÿӃn yӃu tӕ nhiӋWÿӝ WURQJSKѭѫQJSKiSQj\'RÿyêWѭӣng mӟi
cӫa LuұQYăQQKҵPSKiWWULӇn SKѭѫQJSKiS0(0 Yӟi nhiӅXѭXÿLӇPKѫQWURQJÿyFiF
phҫn tӱ tҩm sӁ ÿѭӧF[HPQKѭGLFKX\ӇQYjWҧi trӑQJFyWKӇ ÿѭӧF[HPOjÿӭQJ\rQErQ
cҥQKÿy[pWÿӃn yӃu tӕ nhiӋWÿӝ NKLWiFGөQJOrQFiFPһt cӫa tҩm. LuұQYăQK\Yӑng sӁ
JySSKҫQQjRÿyWURQJQJKLrQFӭu vӅ ӭng xӱ ÿӝng lӵc hӑc cӫa tҩm vұt liӋu chӭFQăQJ
WUrQQӅQSDVWHUQDNFy[pWÿӃn ҧQKKѭӣng cӫa nhiӋWÿӝ.
iii
ABSTRACT
A composite is a material that is synthesized from two or more different materials in
order to create a new material. They are superior and more durable than the original
materials. Functional Graded Materials (FGM) is a special, heterogeneous, isotropic
composite. They have mechanical properties that vary continuously with the thickness
of the plate and they are most commonly used in high temper ature environments.
Typical FGM materials are made up of two components: ceramic and metal. Ceramics
have high elastic modulus, a very small coefficient of thermal expansion and a heat
transfer coefficient. It makes the functional material highly rigid and very inert to heat.
In addition, the metal makes the functional material tough, overcoming the cracking
that occurs due to the brittleness of the ceramic in the high temperature environment.
The advantage of functional materials is the ability to fabricat e structures according to
desired properties under specific working conditions, such as in environments of high
temperature, impact, abrasion, etc. In construction, the plate problem on the pasternak
foundation has high applicability, such as the foundatio n of civil, industrial, traffic,
reactors,... In a short period of time, many problems related to the structural analysis of
FGM plates have been studied, especially the behavior of the plate on the viscoelastic
foundation when subjected to dynamic loads. To analyze the dynamics of the plate
problem on the Pasternak foundation, the plate model on the Paternak foundation was
applied. This study focuses on analyzing the dynamic behavior of FGM sheet structures
according to the Reissner-Mindlin model using the Moving Element Method (MEM)
and considering the influence of temperature. Previous studies usually only model the
plate structure under moving load by analytical method, finite element method -FEM,
and moving element method-MEM, but have not considered the temperature factor in
MEM. Therefore, the new idea of this study is to develop MEM with more advantages,
where the plate elements will be considered as moving and the load can be considered
stationary. Besides, this study considers the temperature factor on the sides of the plate.
This study is expected to contribute to the study of the dynamic behavior of FGM plates
on Pasternak foundations in a temperature environment.
iv
/Ӡ,&$0 Ĉ2$1
7{L[LQFDPÿRDQÿk\OjF{QJYLӋFGRFKtQKW{LWKӵc hiӋQGѭӟi sӵ Kѭӟng dүn cӫa thҫy
TS. Trҫn Minh Thi.
Mӝt sӕ kӃt quҧ trong LuұQYăQÿѭӧFF{QJEӕ trong tҥSFKt1JѭӡL[k\Gӵng (ISSN
FѫTXDQFӫa Tәng hӝL[k\Gӵng ViӋW1DP WKiQJ -2021 sӕ 355&356
QăPWKӭ XXXIV.
%jLEiR³Moving element analysis of FGM plate considering effect of temperature
XQGHUPRYLQJORDG´ÿmQӝSYjÿDQJFKӡ duyӋt tҥi Hӝi nghӏ quӕc tӃ lҫn thӭ hai vӅ kiӃn
WU~FYjF{QJWUuQKGkQGөng bӅn vӳQJ ,&6&($ QăPFKӫ ÿӅ &{QJQJKӋ hiӋQÿҥi
YjViQJWҥRFKR[k\GӵQJYjNLӃQWU~F
KӃt quҧ trong LuұQYăQOjÿ~QJVӵ thұWYjFKѭDÿѭӧFF{QJEӕ ӣ FiFQJKLrQFӭXNKiF
QJRjLFiFF{QJEӕ WUrQ
7{L[LQFKӏXWUiFKQKLӋm vӅ F{QJYLӋc thӵc hiӋn cӫDPuQK
7S+&0 QJj\WKiQJQăP
Trҫn Quang Sӻ
v
MӨC LӨC
1+,ӊ09Ө/8Ұ19Ă17+Ҥ&6Ƭ ...................................................................................i
/Ӡ,&Ҧ0Ѫ1........................................................................................................................ ii
7Ï07Ҳ7/8Ұ19Ă17+Ҥ&6Ƭ ................................................................................... iii
/Ӡ,&$0Ĉ2$1 ..................................................................................................................v
&+ѬѪ1* GIӞI THIӊU .............................................................................................1
1.1.
Giӟi thiӋXVѫOѭӧc vӅ ÿӅ WjLOXұQYăQ .................................................................1
1.1.1.
Ĉһt vҩQÿӅ..........................................................................................................1
1.1.2.
7tQKFҩp thiӃt cӫDÿӅ WjL................................................................................1
1.1.3. 7uQK KuQK Vӱ dөng vұt liӋu biӃQ ÿәi chӭF QăQJ )*0 WURQJQѭӟF Yj
WUrQWKӃ giӟi......................................................................................................................2
1.1.4.
7uQKKuQKQJKLrQFӭXYjWәQJTXDQWjLOLӋu...............................................3
1.1.5.
MөFWLrXÿӕLWѭӧQJYjSKҥPYLQJKLrQFӭu. .............................................4
1.1.5.1. MͭFWLrXQJKLrQFͱu ........................................................................................4
1.1.5.2. Ĉ͙LW˱ͫQJQJKLrQFͱu......................................................................................5
1.1.5.3. Ph̩PYLQJKLrQFͱu .........................................................................................5
1.2.
Giӟi thiӋu cҩXWU~FFӫa luұQYăQ .........................................................................5
&+ѬѪ1* &Ѫ6Ӣ /é7+8<ӂT...............................................................................7
2.1.
%jLWRiQWҩm chӏu tҧi trӑng di chuyӇn. ...............................................................7
2.1.1.
/êWKX\Ӄt tҩm biӃQÿәi chӭFQăQJ)*0 ...................................................7
2.1.2.
BiӃn dҥng cӫa tҩPYjPӕi quҥn hӋ giӳa ӭng suҩWYj biӃn dҥng...........9
2.1.3.
0{KuQKQӅQÿjQQKӟt Pasternak. ............................................................ 10
2.1.4.
TҩP)*0WUrQQӅQÿjQQKӟt Pasternak. ............................................... 11
2.2.
3KѭѫQJSKiS0(0FKREjLWRiQWҩm chӏu tҧi trӑng di chuyӇn. .............. 13
2.2.1.
Phҫn tӱ ÿҷng tham sӕ. ................................................................................. 13
2.2.2. %jL WRiQ WҩP )*0 WUrQ QӅQ ÿjQ QKӟt Pasternak chӏu tҧi trӑng di
chuyӇn. ..................................................................................................................17
2.3. ҦQK Kѭӣng cӫa nhiӋWÿӝ ÿӃn ӭng xӱ ÿӝng tҩP)*0 WUrQQӅn Pasternak
chӏu tҧi trӑng di chuyӇn ................................................................................................. 24
2.4.
3KѭѫQJSKiS1HZPDUN ..................................................................................... 29
&+ѬѪ1* NӜ,'81*3+ѬѪ1*3+È31*+,Ç1&ӬU............................... 32
3.1.
7K{QJVӕ ÿҫXYjRYjWKXұWWRiQVӱ dөng........................................................ 32
vi
3.1.1.
7K{QJVӕ ÿҫXYjR .......................................................................................... 32
3.1.2.
GiҧLEjLWRiQWKHRGҥng gia tӕc .................................................................. 33
3.1.3.
GiҧLEjLWRiQWKHRGҥng chuyӇn vӏ ............................................................ 33
3.1.4.
Ĉӝ әQÿӏQKYjKӝi tө cӫDSKѭѫQJSKiS1HZPDUN ................................ 33
3.2.
/ѭXÿӗ thuұWWRiQ ................................................................................................ 35
&+ѬѪ1* %¬,72È16Ӕ ....................................................................................... 36
4.1.
KiӇm chӭQJFKѭѫQJWUuQK0DWODE ................................................................... 36
4.1.1. %jLWRiQ 3KkQ WtFKӭng xӱ cӫa tҩm FGM khi chӏX WiFGөng cӫa tҧi
trӑQJWƭQK...................................................................................................................... 36
4.1.2.
%jLWRiQ 3KkQWtFKGDRÿӝng cӫa tҩm FGM ...................................... 38
4.1.3. %jLWRiQ 3KkQ WtFKÿӝng lӵc hӑc tҩP)*0 WUrQQӅn Pasternak chӏXWiF
dөng cӫa tҧi trӑQJGLÿӝng. ........................................................................................... 43
4.2. 3KkQ WtFKÿӝng lӵc hӑc tҩP)*0 WUrQQӅn Pasternak chӏXWiFGөng cӫa
tҧi trӑQJGLÿӝQJFy[pWÿӃn ҧQKKѭӣng cӫa nhiӋWÿӝ. ............................................ 44
4.2.1.
't
%jLWRiQ .KҧR ViWVӵ hӝi tө cӫa chuyӇn vӏ WKHREѭӟc lһp thӡi gian
..................................................................................................................44
4.2.2. %jL WRiQ .KҧR ViW ӭng xӱ ÿӝng lӵc hӑc cӫa tҩP )*0 WUrQ QӅn
Pasternak chӏu tҧi trӑQJGLÿӝQJWURQJP{LWUѭӡng nhiӋWÿӝ WKD\ÿәi. ........... 46
4.2.3. %jL WRiQ KhҧR ViW ӭng xӱ ÿӝng lӵc hӑc cӫa tҩP )*0 WUrQ QӅn
Pasternak chӏu tҧi trӑQJGLÿӝQJWURQJP{LWUѭӡng nhiӋWÿӝ khi hӋ sӕ tӍ lӋ thӇ
WtFKQWKD\ÿәi............................................................................................................... 50
4.2.4. %jL WRiQ KhҧR ViW ӭng xӱ ÿӝng lӵc hӑc cӫa tҩP )*0 WUrQ QӅn
Pasternak chӏu tҧi trӑQJGL ÿӝQJ WURQJ P{LWUѭӡng nhiӋW ÿӝ khi chiӅX Gj\ K
WKD\ÿәi. ......................................................................................................................... 52
4.2.5. %jL WRiQ KhҧR ViW ӭng xӱ ÿӝng lӵc hӑc cӫa tҩP )*0 WUrQ QӅn
Pasternak chӏu tҧi trӑQJGLÿӝQJWURQJP{LWUѭӡng nhiӋWÿӝ khi hӋ sӕ ÿӝ cӭng
k wf WKD\ÿәi.................................................................................................................... 54
4.2.6. %jL WRiQ KhҧR ViW ӭng xӱ ÿӝng lӵc hӑc cӫa tҩP )*0 WUrQ QӅn
Pasternak chӏu tҧi trӑQJGLÿӝQJWURQJP{LWUѭӡng nhiӋWÿӝ khi sӭFNKiQJFҳt
k sf WKD\ÿәi..................................................................................................................... 56
4.2.7. %jL WRiQ KhҧR ViWӭng xӱ ÿӝng lӵc hӑc cӫa tҩP )*0 WUrQ QӅn
Pasternak chӏu tҧi trӑQJGLÿӝQJWURQJP{LWUѭӡng nhiӋW ÿӝ khi hӋ sӕ cҧn nӅn
cf WKD\ÿәi. ..................................................................................................................... 57
4.2.8. %jL WRiQ KhҧR ViWӭng xӱ ÿӝng lӵc hӑc cӫa tҩP )*0 WUrQ QӅn
Pasternak chӏu tҧi trӑQJGLÿӝQJWURQJP{LWUѭӡng nhiӋWÿӝ khi lӵc di chuyӇn
3WKD\ÿәi....................................................................................................................... 60
vii
4.2.9. %jL WRiQ KhҧR ViWӭng xӱ ÿӝng lӵc hӑc cӫa tҩP )*0 WUrQ QӅn
Pasternak chӏu tҧi trӑQJGL ÿӝQJ WURQJP{L WUѭӡng nhiӋW ÿӝ NKL WKjQK SKҫn
cҩu tҥo tҩP)*0WKD\ÿәi. ....................................................................................... 62
&+ѬѪ1* KӂT LUҰ19¬.,ӂN NGHӎ............................................................. 66
5.1.
KӃt luұn .................................................................................................................. 66
5.2.
KiӃn nghӏ................................................................................................................ 66
'$1+0Ө&&È&&Ð1*%Ӕ.+2$+Ӑ& ............................................................... 68
7¬,/,ӊU THAM KHҦO ................................................................................................ 88
MӜT SӔ 00$7/$%&+Ë1+ ................................................................................... 94
/é/ӎ&+75Ë&+1*$1* ............................................................................................ 108
viii
DANH MӨC BҦNG BIӆU
Bҧng 2.1: TӑDÿӝ YjWUӑng sӕ FiFÿLӇm Gauss .................................................................. 17
Bҧng 3.1: 7K{QJsӕ tҩm FGM ............................................................................................ 32
Bҧng 3.2: 7K{QJsӕ nӅQKDLWK{QJVӕ Pasternak ............................................................... 32
Bҧng 3.3: 7K{QJsӕ tҧi trӑng............................................................................................... 32
BҧQJ 7K{QJVӕ vұt liӋu FGM ZrO2/Al....................................................................... 37
Bҧng 4.2: ChuyӇn vӏ NK{QJWKӭ QJX\rQWҥLWkPWҩP)*0WKHROѭӟi chia phҫn tӱ. ..... 37
Bҧng 4.3: Tҫn sӕ GDRÿӝng tӵ QJKLrQNK{QJWKӭ QJX\rQY cӫDPRGHGDRÿӝng thӭ nhҩt
tҩP)*0WKHROѭӟi chia phҫn tӱ. ....................................................................................... 38
Bҧng 4.4: BҧQJ VRViQKWҫn sӕ GDRÿӝng tӵ QKLrQNK{QJWKӭ QJX\rQPRGHÿҫXWLrQ
cӫa tҩm vӟL/K YjOѭӟi chia 5x5 ............................................................................... 40
Bҧng 4.5: Tҫn sӕ GDRÿӝng tӵ QKLrQNK{QJWKӭ QJX\rQPRGHGDRÿӝQJÿҫXWLrQFӫa
tҩm FGM vӟLFiFEӅ Gj\NKiFQKDX.................................................................................. 40
Bҧng 4.6: &iFWK{QJVӕ vұt liӋu cӫa tҩP)*0Yj)*0 ............................................. 41
Bҧng 4.7: Tҫn sӕ GDRÿӝng tӵ QKLrQNK{QJWKӭ QJX\rQPRGHGDRÿӝQJÿҫXWLrQFӫa 2
tҩPFyWӍ lӋ Ec/Em NKiFQKDX............................................................................................... 42
Bҧng 4.8: ChuyӇn vӏ tҥLWkPWҩm (10 -5 m) vӟLFiFKӋ sӕ tӍ lӋ thӇ WtFKQNKiFQKDX...... 43
BҧQJ &iF KӋ sӕ phө thuӝc nhiӋWÿӝ cӫDFDUDPLFYjNLPORҥi trong vұt liӋu FGM
(Si3 N4/SUS304) .................................................................................................................... 44
Bҧng 4.10: Sӵ hӝi tө cӫa chuyӇn vӏ (10 -3P WKHRFiFEѭӟc thӡi gian 't....................... 45
BҧQJ 6RViQKFKX\Ӈn vӏ cӫa tҩm FGM khi nhiӋWÿӝ WiFGөQJOrQPһWWKD\ÿәi.
................................................................................................................................................. 46
BҧQJ 6RViQKFKX\Ӈn vӏ cӫa tҩm FGM khi nhiӋWÿӝ WiFGөQJOrQPӝt mһWWKD\ÿәi.
................................................................................................................................................. 48
BҧQJ 6RViQKFKX\Ӈn vӏ ӭng vӟi hӋ sӕ tӍ lӋ vұt liӋu n WKD\ÿәi. ........................... 50
BҧQJ 6RViQKFKX\Ӈn vӏ cӫa tҩm khi chiӅXGj\WҩPKWKD\ÿәi............................ 52
BҧQJ 6RViQKFKX\Ӈn vӏ cӫa tҩm khi hӋ sӕ ÿӝ cӭng nӅn k wf WKD\ÿәi. ............... 54
BҧQJ 6RViQKFKX\Ӈn vӏ cӫa tҩm khi sӭFNKiQJFҳt ksf WKD\ÿәi. ........................ 56
BҧQJ 6RViQKFKX\Ӈn vӏ cӫa tҩm khi sӭFNKiQJFҳt cf WKD\ÿәi. ......................... 58
BҧQJ 6RViQKFKX\Ӈn vӏ cӫa tҩm khi vұn tӕc cӫa lӵc chuyӇQÿӝQJ9WKD\ÿәi. 59
BҧQJ 6RViQh chuyӇn vӏ cӫa tҩm khi lӵc di chuyӇQ3WKD\ÿәi. ........................... 60
ix
BҧQJ &iFKӋ sӕ phө thuӝc nhiӋWÿӝ cӫDFiFORҥi trong vұt liӋu FGM .................. 62
Bҧng 4.21: TӍ sӕ P{ÿXQÿjQKӗi vұt liӋu gӕPYjNLPORҥi cӫDFiFWҩm FGM. ............ 63
BҧQJ 6RViQKFKX\Ӈn vӏ cӫa tҩm khi vұt liӋu tҩP)*0WKD\ÿәi ӣ 300 oK......... 63
BҧQJ 6RViQKFKX\Ӈn vӏ cӫa tҩm khi vұt liӋu tҩP)*0WKD\ÿәi ӣ 400 oK......... 65
x
DANH MӨC +Î1+ ҦNH
Hunh 2.1: Quan hӋ giӳa Vc vӟi tӍ sӕ ]KYjFKӍ sӕ tӍ lӋ thӇ WtFKQ .....................................8
Hunh 2.2: Tҩm FGM trӅn nӅQÿjQQKӟt Pasternak. .......................................................... 11
Hunh 2.3: a. Phҫn tӱ Q9 trong hӋ tӑDÿӝ tәng thӇ (x,y); b. Phҫn tӱ Q9 trong hӋ tӑDÿӝ tӵ
QKLrQ [,K). ............................................................................................................................ 14
Hunh 2.4: Rӡi rҥc tҩPWKjQK1e phҫn tӱ YjKӋ tӑDÿӝ chuyӇQÿӝng (r,s)....................... 18
Hunh 4.1: ChuyӇn vӏ NK{QJWKӭ QJX\rQWKHROѭӟLFKLDSKkQWӱ. .................................... 37
Hunh 4.2: Sӵ hӝi tө tҫn sӕ GDRÿӝng tӵ QJKLrQNK{QJWKӭ QJX\rQY cӫa mode dao
ÿӝng thӭ nhҩt tҩP)*0WKHROѭӟi chia phҫn tӱ. .............................................................. 39
Hunh 4.3: Tҫn sӕ GDRÿӝng tӵ QKLrQNK{QJWKӭ QJX\rQPRGHGDRÿӝQJÿҫXWLrQFӫa
tҩm FGM vӟLFiFEӅ Gj\NKiFQKDX.................................................................................. 41
Hunh 4.4: Tҫn sӕ GDRÿӝng tӵ QKLrQNK{QJWKӭ QJX\rQPRGHGDRÿӝQJÿҫXWLrQFӫa 2
tҩPFyWӍ lӋ Ec/Em NKiFQKDX............................................................................................... 42
Hunh 4.5: ChuyӇn vӏ tҥLWkPWҩm (10 -5 m) vӟLFiFKӋ sӕ tӍ lӋ thӇ WtFKQNKiFQKDX ...... 43
Hunh 4.6: Sӵ hӝi tө cӫa chuyӇn vӏ (10 -3P WKHRFiFEѭӟc thӡi gian 't. ........................ 45
HuQK 6RViQKFKX\Ӈn vӏ cӫa tҩm FGM khi nhiӋWÿӝ WiFGөQJOrQPһWWKD\ÿәi. 47
HuQK 6RViQKFKX\Ӈn vӏ cӫa tҩm FGM khi nhiӋWÿӝ WiFGөQJOrQPһWGѭӟi thay
ÿәi. .......................................................................................................................................... 48
HuQK 6RViQKFKX\Ӈn vӏ cӫa tҩm FGM khi nhiӋWÿӝ WiFGөQJOrQPһWWUrQWKD\ÿәi.
................................................................................................................................................. 49
Hunh 4.10: ChuyӇn vӏ lӟn nhҩt cӫa tҩm khi nhiӋWÿӝ WiFGөQJOrQPһWGѭӟLWKD\ÿәi. 49
Hunh 4.11: ChuyӇn vӏ lӟn nhҩt cӫa tҩm khi nhiӋWÿӝ WiFGөng OrQPһWWUrQWKD\ÿәi. . 50
HuQK 6RViQKFKX\Ӈn vӏ ӭng vӟi hӋ sӕ tӍ lӋ thӇ WtFK n WKD\ÿәi............................. 51
Hunh 4.13: ChuyӇn vӏ lӟn nhҩt cӫa tҩm ӭng vӟi hӋ sӕ tӍ lӋ thӇ WtFK n WKD\ÿәi. ........... 51
HuQK 6RViQKFKX\Ӈn vӏ cӫa tҩm khi chiӅXGj\KWKD\ÿәi.................................... 53
Hunh 4.15: ChuyӇn vӏ lӟn nhҩt cӫa tҩm ӭng vӟLFiFJLiWUӏ chiӅXGj\KWKD\ÿәi. ....... 53
HuQK 6RViQKFKX\Ӈn vӏ cӫa tҩm khi hӋ sӕ ÿӝ cӭng nӅn k wf WKD\ÿәi................. 55
Hunh 4.17: ChuyӇn vӏ lӟn nhҩt cӫa tҩm ӭng vӟLFiFJLiWUӏ ÿӝ cӭng nӅn k wf WKD\ÿәi. 55
HuQK 6RViQKFKX\Ӈn vӏ cӫa tҩm khi sӭFNKiQJFҳt ksf WKD\ÿәi.......................... 56
xi
Hunh 4.19: ChuyӇn vӏ lӟn nhҩt cӫa tҩm ӭng vӟLFiFJLiWUӏ sӭFNKiQJFҳt k sf WKD\ÿәi.
................................................................................................................................................. 57
Hunh 4.20: 6RViQKFKX\Ӈn vӏ cӫa tҩm khi hӋ sӕ cҧn nӅn cf WKD\ÿәi. .......................... 58
Hunh 4.21: ChuyӇn vӏ lӟn nhҩt cӫa tҩm ӭng vӟLFiFJLiWUӏ hӋ sӕ cҧn cf WKD\ÿәi. ....... 58
HuQK 6RViQKFKX\Ӈn vӏ cӫa tҩm khi vұn tӕc cӫa lӵc chuyӇQÿӝQJ9WKD\ÿәi.. 59
Hunh 4.23: ChuyӇn vӏ lӟn nhҩt cӫa tҩm ӭng vӟLFiFJLiWUӏ vұn tӕF9WKD\ÿәi. .......... 60
HuQK 6RViQKFKX\Ӈn vӏ cӫa tҩPNKLÿӝ lӟn lӵc di chuyӇQ3WKD\ÿәi. ............... 61
Hunh 4.25: ChuyӇn vӏ lӟn nhҩt cӫa tҩm ӭng vӟLFiFJLiWUӏ ÿӝ lӟn lӵF3WKD\ÿәi. ...... 61
HuQK 6RViQKFKX\Ӈn vӏ cӫa tҩm khi vұt liӋu tҩP)*0WKD\ÿәi ӣ 300 oK. ........ 64
HuQK 6RViQKFKX\Ӈn vӏ cӫa tҩm khi vұt liӋu tҩP)*0WKD\ÿәi ӣ 400 oK. ........ 65
xii
'$1+ 0Ө& 0Ӝ7 6Ӕ.é +,ӊ89,ӂ7 7Ҳ7
Chӳ viӃt tҳt
FGM
Tҩm biӃQÿәi chӭFQăQJ Functional Graded Materials)
MEM
3KѭѫQJ SKiSSKҫn tӱ chuyӇQÿӝng (Moving Element Method)
Q9
Phҫn tӱ tӭ JLiF Q~W 4XDGULODWHUDOQLQH-node element)
FEM
3KѭѫQJ SKiSSKҫn tӱ hӳu hҥn (Finite Element Method)
FEM-9
3KѭѫQJ SKiSSKҫn tӱ hӳu hҥn sӱ dөng phҫn tӱ Q~W
DOF
Bұc tӵ do (Degree of Freedom)
HSDT
FSDT
/ê WKX\Ӄt biӃn dҥng cҳt bұc cao (Higher-Order Shear Deformation
Theory)
/ê thuyӃt biӃn dҥng cҳt bұc nhҩt (First-Order Shear Deformation
Theory)
Ma trұQYjYpFWѫ
u
9pFWѫFKX\Ӈn vӏ tҥi mӝWÿLӇm bҩt kǤ cӫa kӃt cҩu tҩm
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9pFWѫÿӝ cong
d
9pFWѫFKX\Ӈn vӏ Q~WFӫa phҫn tӱ
Ȗ
Ma trұn biӃn dҥng cҳt
M
Ma trұn khӕLOѭӧng tәng thӇ
K
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C
Ma trұn cҧn tәng thӇ
Me
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.êKLӋu
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ChiӅXGjLWҩPWKHRSKѭѫQJ x
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9ұQWӕFFӫDWҧLWUӑQJGLÿӝQJ
I,x
ĈҥRKjPULrQJEұFPӝWFӫDKjPI WKHRELӃQ x
I,xx
ĈҥRKjPULrQJEұFKDLFӫDKjP I WKHRELӃQ x
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ĈҥRKjPULrQJEұFKDLFӫDKjP I WKHRELӃQ x Yj y
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xiv
&KѭѫQJ *Lӟi thiӋu
&+ѬѪ1*
1.1.
GIӞI THIӊU
Giӟi thiӋXVѫOѭӧc vӅ ÿӅ WjLOXұQYăQ
1.1.1. Ĉһt vҩQÿӅ
Vұt liӋu biӃQ ÿәi chӭF QăQJ )XQFWLRQDOO\ *UDGHG 0DWHULDO ± )*0 Oj Yұt liӋu
composite thӃ hӋ mӟLÿѭӧc mӝWQKyPQKjNKRDKӑc Nhұt Bҧn giӟi thiӋXYjRQăP
TҩP)*0 ÿmNKҳc phөFÿѭӧc hiӋQWѭӧng tұp trung ӭng suҩWYjKLӋQWѭӧQJWiFKOӟp cӫa
tҩm composite.
Nhӡ YjRQKӳQJÿһFWtQKѭXYLӋWPjYұt liӋX)*0 ÿmÿѭӧc ӭng dөng trong nhiӅXOƭQK
vӵF9uYұ\PjQKLӅXQJKLrQFӭu vӅ ӭng xӱ cӫa tҩP)*0ÿѭӧFFiFQKjNKRDKӑFF{QJ
bӕ trong nhӳQJ QăP JҫQ ÿk\EҵQJ FiFSKѭѫQJ SKiSQKѭSKѭѫQJ SKiS5LW] SKѭѫQJ
SKiSYLSKkQFҫXSKѭѫQJSKѭѫQJSKiSSKҫn tӱ hӳu hҥQWX\QKLrQFiFSKѭѫQJSKiS
Qj\FyPӝWYjLKҥn chӃÿӇ khҳc phөFFiFKҥn chӃ Qj\.RKYjFӝng sӵ >@ÿmÿӅ xuҩt
SKѭѫQJSKiSSKҫn tӱ chuyӇQÿӝng (Moving Element Method ± 0(0 FKREjLWRiQӭng
xӱ dҫPYjWҩm chӏu tҧi trӑQJGLÿӝng. So vӟLFiFF{QJWUuQKQJKLrQFӭu vӅ ӭng xӱ WƭQK
YjGDRÿӝng cӫa tҩP)*0 QJKLrQFӭu vӅ ӭng xӱ ÿӝng cӫa tҩm FGM chӏu tҧi trӑng di
chuyӇQFKѭDÿѭӧc thӵc hiӋn nhiӅXÿһc biӋWFKѭDFyQJKLrQFӭXSKkQWtFKӭng xӱ cӫa
tҩm FGM chӏu tҧi trӑng di chuyӇQFy[pWÿӃn ҧQKKѭӣng cӫa nhiӋWÿӝ sӱ dөQJSKѭѫQJ
SKiS0(0 /XұQYăQFӫa hӑFYLrQVӁ WUuQKEj\ÿӅ WjLQj\
1.1.2. 7tQK Fҩp thiӃt cӫDÿӅ WjL
7iFGөng cӫa tҧi trӑQJWKD\ÿәi theo thӡLJLDQYjWKD\ÿәi theo vӏ WUtWUrQNӃt cҩXF{QJ
WUuQKOLrQTXDQÿӃQÿӝng lӵc hӑFF{QJWUuQK+ѭӟQJ QJKLrQFӭXQj\FyVӭc hҩp dүn lӟn
YjQKұQÿѭӧc sӵ TXDQWkPFӫa nhiӅXQKjNKRDKӑc. Vӟi sӵ SKiWWULӇn cӫa khoa hӑc kӻ
thuұWQJj\QD\FiFF{QJWUuQKÿѭӧF [k\GӵQJQJj\FjQJKLӋQÿҥLKѫQYjYLӋFQJKLrQ
cӭXÿӃn ӭng xӱ ÿӝng cӫa kӃt cҩXF{QJWUuQKFҫn phҧLÿѭӧFTXDQWkPFK~WUӑng nhiӅu
KѫQ0{KuQKNӃt cҩu tҩPWUrQQӅQÿjQQKӟt chӏu tҧi trӑng di chuyӇQFyӭng dөQJNKi
nhiӅu trong thӵc tiӉQQKѭ[HFKҥ\WUrQPһWÿѭӡQJKD\Pi\ED\FKX\ӇQÿӝQJWUrQÿѭӡng
EăQJ&KtQKYuVӵ ӭng dөng rӝng UmLWURQJWKӵc tiӉQQrQWURQJPӝt khoҧng thӡi gian
ngҳQFyUҩt nhiӅXQJKLrQFӭu vӅ ӭng xӱ cӫa tҩPGѭӟLWiFÿӝng cӫa tҧi trӑng di chuyӇn
ÿѭӧFF{QJEӕ vӟi viӋc sӱ dөng nhiӅXSKѭѫQJSKiSSKkQWtFKNKiFQKDXĈҫXWLrQSKҧi
kӇ ÿӃQSKѭѫQJSKiSJLҧLWtFKSKѭѫQJ SKiSQj\FKRUDOӡi giҧLFKtQK[iFQKѭQJJһSNKy
1
&KѭѫQJ *Lӟi thiӋu
NKăQYjFyWKӇ dүQÿӃn bӃ tҳFÿӕi vӟLFiFEjLWRiQSKӭc tҥSQKѭKӋ FyQKLӅu bұc tӵ do,
chuyӇQÿӝQJFyJLDWӕc hoһFFy[pWÿӃn ӭng xӱ phi tuyӃQYuYұ\PjSKѭѫQJSKiSSKҫn
tӱ hӳu hҥn (Finite Element Method ± )(0 ÿѭӧc sӱ dөng phә biӃQÿӇ khҳc phөc nhӳng
ÿLӇm yӃXWUrQ7X\QKLrQÿӕi vӟLFiFEjLWRiQNӃt cҩXFyFKLӅXGjLOӟQQKѭÿѭӡQJ{W{
ÿѭӡQJEăQJVkQED\ WKuFK~QJÿѭӧc giҧ thuyӃWOjWҩPGjLY{KҥQWURQJNKLP{KuQK
WtQKWRiQWKHRSKѭѫQJSKiS)(0OjKӳu hҥQQrQWҧi trӑng sӁ QKDQKFKyQJÿӃn vӏ WUtELrQ
cӫDP{KuQKÿӇ khҳc phөc hҥn chӃ WUrQFyWKӇ P{KuQKNӃt cҩXFyFKLӅXGjLÿӫ lӟn tuy
QKLrQWKӡLJLDQWtQKWRiQVӁ JLDWăQJYj\rXFҫu cҩXKuQKPi\WtQKFDR'RÿyYLӋFÿӅ
xuҩt mӝW SKѭѫQJ SKiSPӟi khҳc phөFFiF Kҥn chӃ WUrQ Oj Y{FQJ Fҫn thiӃt, tӯ ÿy
SKѭѫQJSKiSSKҫn tӱ chuyӇQÿӝQJ0(0 ÿѭӧFUDÿӡLÿӇ giҧi quyӃWFiFEjLWRiQSKkQ
WtFKӭng xӱ kӃt cҩu dҫPYjWҩm chӏu tҧi trӑng di chuyӇQ&iFEjLWRiQQj\VӁ ÿѭӧc giҧi
quyӃWÿѫQJLҧQKѫQYӅ thuұWWRiQYjtWWӕn NpPKѫQYӅ FKLSKtWtQKWRiQPi\WtQK%rQ
cҥQKÿyYLӋc ӭng dөng vұt liӋu mӟi FGM trong cuӝc sӕQJQJj\FjQJSKә biӃQYuYұy
viӋFQJKLrQFӭu vӅ ӭng xӱ ÿӝng cӫDQyÿѭӧc nhiӅXQKjQJKLrQFӭXTXDQWkPYjSKiW
triӇn.
1.1.3. 7uQK KuQK Vӱ dөng vұt liӋu biӃQÿәi chӭFQăQJ)*0 WURQJQѭӟF YjWUrQ
thӃ giӟi.
1Jj\QD\YLӋFWuPNLӃPQJKLrQFӭu ӭng dөQJFiFORҥi vұt liӋu mӟLFyFiFWtQKFKҩt
NKiFELӋt dҫn thay thӃ FiFORҥi vұt liӋu truyӅn thӕQJOj[XWKӃ cӫa thӡLÿҥi hiӋn nay. Vұt
liӋX)*0 ÿѭӧc biӃWÿӃQQKѭORҥi vұt liӋu composite thӃ hӋ mӟLÿѭӧc ӭng dөng trong
OƭQKYӵFKjQJNK{QJ FKӃ tҥRWKkQYӓ Pi\ED\ WURQJ\Kӑc (chӃ tҥRUăQJ[ѭѫQJQKkQ
tҥo), trong quӕFSKzQJ iRJLiSFKӕQJÿҥQ WURQJF{QJQJKLӋSQăQJOѭӧng (tҩPFiFK
nhiӋWWXDELQOzSKҧn ӭQJ YjWURQJ[k\Gӵng. )*0 WKѭӡQJÿѭӧc chӃ tҥo tӯ hӛn hӧp
gӗm gӕP YjNLPORҥLÿk\OjYұt liӋXÿҷQJKѭӟQJQKѭQJNK{QJÿӗng nhҩW9uYұy viӋc
sӱ dөng tҩm vұt liӋXQj\ÿDQJQJj\FjQJSKә biӃQWUrQWKӃ giӟi.
Ӣ QѭӟFWDWKHR[XKѭӟng sӱ dөng vұt liӋXFRPSRVLWHWURQJ[k\Gӵng, chӃ tҥo, an ninh
quӕFSKzQJYұt liӋu biӃQÿәi chӭFQăQJ)*0FNJQJEҳWÿҫXÿѭӧc sӱ dөQJQKѭFKӃ tҥo
ÿҥQÿҥRWrQOӱDYjÿһc biӋWOjFiFNӃt cҩu tҩm vӓ WURQJFiFOzSKҧn ӭng hҥWQKkQVӟi
[XKѭӟQJ[k\GӵQJYjSKiWWULӇQQKjPi\ÿLӋn hҥWQKkQQJj\QD\YLӋFQJKLrQFӭXYj
2
&KѭѫQJ *Lӟi thiӋu
ÿjRWҥRQKkQOӵFFyWUuQKÿӝ FKX\rQP{QFDRYӅ FGM rҩt cҫQÿѭӧFTXDQWkPWULӇn khai
ӣ ViӋt Nam.
1.1.4. 7uQK KuQK QJKLrQ FӭXYjWәQJTXDQ WjLOLӋu.
&iFNӃt cҩu dҥng tҩPWKѭӡnJÿѭӧFP{ KuQKWUrQQӅQÿjQQKӟt chӏXWiFGөng cӫa tҧi
trӑng di chuyӇn. NӝLGXQJQj\ÿѭӧc nhiӅXQKjNKRDKӑFQJKLrQFӭu thӵc hiӋn sӱ dөng
nhiӅXSKѭѫQJSKiSNKiFQKDX
8\PD] Yj Fӝng sӵ >@ ÿm NKҧR ViW GDR ÿӝng cӫa tҩP )*0 YX{QJ YӟL FiF
ÿLӅu kiӋQ ELrQ NKiF QKDX Vӱ dөQJ SKѭѫQJ SKiS 5LW] Yj F{QJ WKӭc chuyӇn vӏ
&KHE\VKHY6DXÿy$WPDQHYjFӝng sӵ >@ÿmÿӅ xuҩt mӝWOêWKX\Ӄt biӃn dҥng cҳt mӟi
ÿӇ SKkQ WtFK GDR ÿӝng cӫa tҩP )*0 WUrQ QӅn Pasternak sӱ dөQJ SKѭѫQJ SKiS
1DYLHU =HQNRXU Yj 5DGZDQ >@ ÿm WUuQK Ej\ QJKLrQ Fӭu tәQJ TXiWYӅ ӭng xӱ WƭQK
YjGDRÿӝng cӫa tҩP)*0 WUrQQӅn Pasternak vӟLOêWKX\Ӄt biӃn dҥng cҳt sӱ dөQJKjP
hyperbolic. 7KDLYj9R >@ÿmSKiWWULӇQOêWKX\Ӄt biӃn dҥng cҳWWKHRKjPVLQFKREjL
WRiQSKkQWtFKXӕn, әQÿӏQKYjGDRÿӝng cӫa tҩm FGM YjEҵQJSKѭѫQJSKiS[k\Gӵng
dӵDWUrQOêWKX\Ӄt biӃn dҥng cҳt bұc nhҩW )6'7 0HOHN]DGHKYj0RQDMMHP]DGHK>@
lҫQOѭӧWÿmSKkQWtFKӭng xӱ cӫa tҩP )*0 WURQJP{LWUѭӡng nhiӋWÿӝ Yjӭng xӱ phi
tuyӃn cӫa tҩm FGM chӏu tҧi trӑng di chuyӇn.
&iF F{QJ WUuQK QJKLrQFӭX WUrQÿӅu sӱ dөQJ SKѭѫQJ SKiSJLҧL WtFKÿӇ WuP QJKLӋm
FKtQK[iFQKѭQJWURQJFiFEjLWRiQSKӭc tҥSQKѭKӋ nhiӅu bұc tӵ do hay chuyӇQÿӝng
NK{QJÿӅXWKuJһp nhiӅXNKyNKăQYjFyWKӇ dүQÿӃn bӃ tҳF9uYұ\PjEjLWRiQVӱ dөng
SKѭѫQJSKiSJLҧLWtFK rҩWtWÿѭӧc sӱ dөQJWURQJFiFEjLWRiQÿӝng cӫa kӃt cҩu phӭc tҥp
trong thӵc tӃ. Vӟi sӵ SKiWWULӇn cӫDPi\WtQKQKLӅXQKjNKRDKӑFÿmJLҧi quyӃWEjLWRiQ
ÿӝng lӵc hӑc kӃt cҩu bҵQJSKѭѫQJSKiSVӕ PjFө thӇ OjSKѭѫQJSKiSSKҫn tӱ hӳu hҥn
(Finite Element Method ± FEM). 6KDKLG]DGHKYjFӝng sӵ >@ÿmSKkQWtFKӭng xӱ cӫa
tҩP)*0 YX{QJYӟLFiFÿLӅu kiӋQELrQNKiFQKDXEҵQJSKѭѫQJSKiSSKҫn tӱ hӳu hҥn
sӱ dөng phҫn mӅP $EDFXVYj )RUWUDQ6DUDGD3UDVDG3DULGDYjFӝng sӵ > @ÿmSKkQ
WtFKӭng xӱ ÿӝng cӫa dҫm FGM tronJP{LWUѭӡng nhiӋWÿӝ cao bҵQJSKѭѫQJSKiSSKҫn
tӱ hӳu hҥn.
3
&KѭѫQJ *Lӟi thiӋu
3KѭѫQJ SKiSSKҫn tӱ hӳu hҥQOjPӝWF{QJFө mҥnh mӁ ÿѭӧc sӱ dөng rҩt nhiӅu trong
EjLWRiQSKkQWtFKӭng xӱ kӃt cҩX7URQJSKѭѫQJSKiSQj\FiFSKҫn tӱ ÿѭӧc thiӃt lұp
sӱ dөng hӋ tӑDÿӝ cӕ ÿӏQKQrn khi tҧi trӑng di chuyӇn cҫn phҧi cұp nhұt lҥi vӏ WUtWҧi
trӑng sau mӛLEѭӟc thӡLJLDQ%rQFҥQKÿyYӟLFiFEjLWRiQWҧi trӑng di chuyӇQWUrQNӃt
cҩXFyFKLӅXGjLOӟQPjP{KuQKWtQKWRiQFӫa kӃt cҩXWURQJSKѭѫQJSKiS)(0FyFKLӅu
GjLKӳu hҥQÿLӅXÿyJk\UDNKyNKăQNKLWҧi trӑng di chuyӇQÿӃQYQJELrQYjYѭӧt ra
QJRjLELrQFӫDP{KuQKWtQKWRiQ&iFNӃt quҧ WtQKWRiQJҫQ ELrQÿѭӧc loҥi bӓ YuVӵ
NK{QJFKtQK[iFGRҧQKKѭӣng cӫDÿLӅu kiӋQELrQ7URQJFӕ gҳQJÿӇ khҳc phөc hҥn chӃ
WUrQSKѭѫQJSKiSFҳWYjGiQ &XW-and-SDVWH)(00HWKRG ÿѭӧFÿӅ xuҩWQKѭQJÿzLKӓi
FiFSKҫn tӱ phҧLFyFKLӅXGjLJLӕQJQKDXĈLӅXQj\VӁ NK{QJWK{QJGөng vӟLEjLWRiQ
FyQKLӅu tҧi trӑng di chuyӇn vӟLFiFNKRҧQJFiFKNKiFQKDX*ҫQÿk\ÿӇ khҳc phөc hҥn
chӃ WUrQFӫDFiFSKѭѫQJ SKiS.RK YjFӝng sӵ >@ÿmÿӅ xuҩWSKѭѫQJ SKiSSKҫn tӱ
chuyӇQÿӝQJ 0(0 FKRP{KuQKGҫm ray chӏu tҧi trӑng di chuyӇQÿӇ SKkQWtFKӭng xӱ
cӫa hӋ thӕQJWjXFDRWӕFYjVDXÿy.RKYjFӝng sӵ [10,11] lҫQOѭӧWÿmSKiWWULӇQSKѭѫQJ
SKiS0(0 FKREjLWRiQSKkQWtFKӭng xӱ tҩPKuQKYjQKNKăQYjӭng xӱ cӫa nӅQEiQ
NK{QJJLDQÿjQKӗi chӏu tҧi trӑng di chuyӇQĈӕi vӟLEjLWRiQSKkQWtFKӭng xӱ cӫa tҩm
vұt liӋu biӃQÿәi chӭF QăQJ)*0 EҵQJ SKѭѫQJ SKiSSKҫn tӱ chuyӇQÿӝng, gҫQ ÿk\
WURQJQJKLrQFӭu cӫD/XRQJYjFӝng sӵ >@ÿmOҫQOѭӧWWUuQKEj\SKѭѫQJSKiSSKҫn tӱ
chuyӇQÿӝng (MEM ÿӇ SKkQWtFKÿӝng tҩP)*0 WUrQQӅn Pasternak chӏu tҧLÿLӅXKzD
chuyӇQÿӝQJYjWURQJEjLWRiQSKkQWtFKӭng xӱ cӫa tҩm vұt liӋu chӭFQăQJ)*0 WUrQ
nӅn Pasternak chӏu tҧi trӑng di chuyӇn.
1KuQFKXng, so vӟLFiFF{QJWUuQKYӅ QJKLrQFӭu ӭng xӱ WƭQKYjGDRÿӝng cӫa tҩm
)*0 QJKLrQFӭu vӅ ӭng xӱ ÿӝng cӫa tҩm FGM chӏu tҧi trӑng di chuyӇQFKѭDÿѭӧc
thӵc hiӋn nhiӅu. Cө thӇ SKkQWtFKӭng xӱ cӫa tҩm FGM chӏu tҧi trӑng di chuyӇQFy[pW
ÿӃn ҧQKKѭӣng cӫa nhiӋWÿӝ bҵQJSKѭѫQJSKiS0(0 FKѭDÿѭӧFÿӅ cұp. LuұQYăQVӁ
WUuQKEj\U}YӅ vҩQÿӅ Qj\
1.1.5. MөFWLrXÿӕLWѭӧQJ YjSKҥP YLQJKLrQFӭu.
1.1.5.1.
MͭFWLrXQJKLrQ Fͱu
4
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