João Paulo Canha da Silva
DETERMINAÇÃO DE CARGAS DE COLAPSO:
ANÁLISE INCREMENTAL VERSUS ANÁLISE
LIMITE
Dissertação para obtenção do Grau de Mestre em Engenharia Civil
Orientador: Professor Doutor Mário Vicente da Silva
Júri:
Presidente:Prof. Doutor Corneliu Cismasiu Arguente: Prof. Doutora Zuzana Dimitrovová
✐
✧❈♦♣②r✐❣❤t✧❏♦ã♦ P❛✉❧♦ ❈❛♥❤❛ ❞❛ ❙✐❧✈❛✱ ❋❈❚✴❯◆▲ ❡ ❯◆▲
✐✐✐
❘❡s✉♠♦
❆ ❆♥á❧✐s❡ ■♥❝r❡♠❡♥t❛❧ ❡ ❛ ❆♥á❧✐s❡ ▲✐♠✐t❡ sã♦ ♦s ♣r✐♥❝✐♣❛✐s ♠ét♦❞♦s ✉t✐❧✐③❛❞♦s ♥❛ ❞❡t❡r♠✐♥❛çã♦ ❞❛ ♠á①✐♠❛ ❝❛r❣❛ s✉♣♦rt❛❞❛ ♣♦r ✉♠❛ ❡str✉t✉r❛ ❝❛r❛❝t❡r✐③❛❞❛ ♣♦r ✉♠ ❝♦♠♣♦rt❛♠❡♥t♦ ♣❧ást✐❝♦✳ ❖ ❛♣❛r❡❝✐♠❡♥t♦ ❞❡ s♦❢t✇❛r❡s ❞❡ ❡❧❡♠❡♥t♦s ✜♥✐t♦s ✈❡✐♦ tr❛③❡r ✉♠❛ ❡♥♦r♠❡ ❡✈♦❧✉çã♦ ♥❡st❡ ❝❛♠♣♦✳
◆❡st❡ tr❛❜❛❧❤♦ é ❛✈❛❧✐❛❞❛ ❛ q✉❛❧✐❞❛❞❡ ❞♦s ❞♦✐s ♠ét♦❞♦s ♣r♦❝✉r❛♥❞♦ ❛♥❛❧✐s❛r✲s❡ ❞♦✐s ❛s♣❡❝t♦s ❢✉♥❞❛♠❡♥t❛✐s✿ ❛ q✉❛❧✐❞❛❞❡ ❞❛ s♦❧✉çã♦ ❡ ❛ s✉❛ ❡✜❝✐ê♥❝✐❛✳ ❯t✐❧✐③❛r❛♠✲s❡ três s♦❢t✇❛r❡s ❞✐st✐♥t♦s✱ ❆◆❙❨❙ ❡ P❧❛①✐s ♣❛r❛ ❡st✉❞♦s ♣r❡❝♦♥✐③❛♥❞♦ ✉♠❛ ❛♥á❧✐s❡ ✐♥❝r❡⑧ ♠❡♥t❛❧ ❞❡ ❝❛r❣❛ ❡ ♦ s♦❢t✇❛r❡ ❙❯❇▲■▼✸❞ ♣❛r❛ ❡st✉❞♦s r❡s✉❧t❛♥t❡s ❞❡ ✉♠❛ ❛♥á❧✐s❡ ❧✐♠✐t❡✱ q✉❡ t❡♠ ❝♦♠♦ ❜❛s❡ ❞❛ s✉❛ ❢♦r♠✉❧❛çã♦ ♦ ❚❡♦r❡♠❛ ❈✐♥❡♠át✐❝♦✳
✈
❆❜str❛❝t
■♥❝r❡♠❡♥t❛❧ ❆♥❛❧②s✐s ❛♥❞ ▲✐♠✐t ❆♥❛❧②s✐s ❛r❡ t❤❡ ♠❛✐♥ ♠❡t❤♦❞s ✉s❡❞ ❢♦r ❞❡t❡r♠✐♥✐♥❣ t❤❡ ♠❛①✐♠✉♠ ❧♦❛❞ s✉♣♣♦rt❡❞ ❜② ❛ str✉❝t✉r❡ ❝❤❛r❛❝t❡r✐③❡❞ ❜② ❛ ♣❧❛st✐❝ ❜❡❤❛✈✐♦r✳ ❚❤❡ ❛♣♣❡❛r❛♥❝❡ ♦❢ ✜♥✐t❡ ❡❧❡♠❡♥t s♦❢t✇❛r❡s ❤❛s ❜r♦✉❣❤t s✐❣♥✐✜❝❛♥t ❞❡✈❡❧♦♣♠❡♥t ✐♥ t❤✐s ✜❡❧❞✳
❚❤✐s ✇♦r❦ ❡✈❛❧✉❛t❡s t❤❡ q✉❛❧✐t② ♦❢ ❜♦t❤ ♠❡t❤♦❞s ❜② ❛♥❛❧②③✐♥❣ t✇♦ ❜❛s✐❝ ❛s♣❡❝ts✿ t❤❡ s♦❧✉t✐♦♥✬s q✉❛❧✐t② ❛♥❞ t❤❡ ❡✣❝✐❡♥❝② ♦❢ t❤❡ ❛♥❛❧②s✐s✳ ❚❤❡r❡ ❛r❡ ✉s❡❞ t❤r❡❡ ❞✐✛❡r❡♥t s♦❢t✇❛r❡s✱ ❆◆❙❨❙ ❛♥❞ P❧❛①✐s ❢♦r st✉❞✐❡s ❛❞✈♦❝❛t✐♥❣ ❛♥ ✐♥❝r❡♠❡♥t❛❧ ❧♦❛❞ ❛♥❛❧②s✐s ❛♥❞ ❙❯❇▲■▼✸❞ s♦❢t✇❛r❡ ❢♦r st✉❞✐❡s r❡s✉❧t✐♥❣ ❢r♦♠ ❛ ❧✐♠✐t ❛♥❛❧②s✐s✱ ✇❤✐❝❤ ✐s ❜❛s❡❞ ✐♥ ✐ts ❢♦r♠✉❧❛t✐♦♥ ♦♥ t❤❡ ❑✐♥❡♠❛t✐❝ ❚❤❡♦r❡♠✳
✈✐✐
P❛❧❛✈r❛s ❈❤❛✈❡
❆♥á❧✐s❡ ▲✐♠✐t❡ ❆♥á❧✐s❡ ■♥❝r❡♠❡♥t❛❧ ❚❡♦r❡♠❛ ❈✐♥❡♠át✐❝♦ P❧❛st✐❝✐❞❛❞❡
❊❧❡♠❡♥t♦s ❋✐♥✐t♦s
❑❡②✇♦r❞s
▲✐♠✐t ❆♥❛❧②s✐s ■♥❝r❡♠❡♥t❛❧ ❆♥❛❧②s✐s
❑✐♥❡♠❛t✐❝ ✭❯♣♣❡r ❇♦✉♥❞✮ ❚❤❡♦r❡♠ P❧❛st✐❝✐t②
✐①
❆❣r❛❞❡❝✐♠❡♥t♦s
❆ r❡❛❧✐③❛çã♦ ❞❡st❛ t❡s❡ ♥ã♦ s❡r✐❛ ♣♦ssí✈❡❧ s❡♠ ♦ ❝♦♥tr✐❜✉t♦ ❞✐r❡❝t♦ ♦✉ ✐♥❞✐r❡❝t♦ ❞❡ ❛❧❣✉♠❛s ♣❡ss♦❛s✱ às q✉❛✐s ❡✉ ❣♦st❛r✐❛ ❞❡ ❡①♣r❡ss❛r ♦ ♠❡✉ ❛❣r❛❞❡❝✐♠❡♥t♦✳
❈♦♠❡ç♦ ♣♦r ❛❣r❛❞❡❝❡r ❛♦ ♠❡✉ ♦r✐❡♥t❛❞♦r ❝✐❡♥tí✜❝♦✱ ♦ Pr♦❢❡ss♦r ▼ár✐♦ ❱✐❝❡♥t❡ ❞❛ ❙✐❧✈❛✳ ❆q✉✐ ❡①♣r❡ss♦ ♦ ♠❡✉ s✐♥❝❡r♦ ❛❣r❛❞❡❝✐♠❡♥t♦ ♣❡❧♦ q✉❡ ♠❡ ❡♥s✐♥♦✉ ❛♦ ❧♦♥❣♦ ❞❡st❡s ♠❡s❡s ❡ ♣❡❧❛ ❢♦r♠❛ ♦r❣❛♥✐③❛❞❛ ❝♦♠♦ ♠❡ ❛❥✉❞♦✉ ❛ ❞❡s❡♥✈♦❧✈❡r ❡st❡ tr❛❜❛❧❤♦✳ ❘❡✈❡❧♦✉ s❡♠♣r❡ ✉♠❛ ❝❛♣❛❝✐❞❛❞❡ ♠✉✐t♦ ❣r❛♥❞❡ ❞❡ ♠❡ ✐♥❝❡♥t✐✈❛r ❛ ❝✉♠♣r✐r ❛♦ ♠á①✐♠♦ t✉❞♦ ♦ q✉❡ tí♥❤❛♠♦s ✐❞❡❛❧✐③❛❞♦ ♣❛r❛ ❡st❛ t❡s❡✳ ❆❣r❛❞❡ç♦ ❛❝✐♠❛ ❞❡ t✉❞♦ ❛ ❡♥♦r♠❡ ❞✐s♣♦♥✐❜✐❧✐❞❛❞❡ q✉❡ s❡♠♣r❡ ❞❡♠♦♥str♦✉ ❡ s❡♠ ❛ q✉❛❧ ❡st❡ tr❛❜❛❧❤♦ t❡r✐❛ s✐❞♦ ♠❛✐s ❞❡♠♦r❛❞♦✳
❆❣r❛❞❡ç♦ t❛♠❜é♠ ❛♦s ♠❡✉s ❛♠✐❣♦s ❡ ❝♦❧❡❣❛s ❞❡ ❡st✉❞♦✱ ▼✐❣✉❡❧✱ ❉❛✈✐❞✱ ❋✐❧✐♣❡✱ ❆❧✈✐t♦ ❡ ❘♦❧❛♥❞✱ ♣♦r t✉❞♦ ♦ q✉❡ ♠❡ ❡♥s✐♥❛r❛♠ ❡ ❛❥✉❞❛r❛♠✱ ♥ã♦ só ❛♦ ❧♦♥❣♦ ❞❛ r❡❛❧✐③❛çã♦ ❞❡st❡ tr❛❜❛❧❤♦ ❝♦♠♦ t❛♠❜é♠ ❛♦ ❧♦♥❣♦ ❞❡ t♦❞♦ ♦ ❝✉rs♦✳
❆ t♦❞♦s ♦s ♠❡✉s ❛♠✐❣♦s✱ ❆r❛ú❥♦✱ ❍❡♥r✐q✉❡✱ ❆♥tó♥✐♦ ❡ ❛♦ ❣r✉♣♦ t♦❞♦ ♣❡❧❛s ✐♥ú♠❡r❛s ❤♦r❛s ❞❡ ❞❡s❝♦♥tr❛❝çã♦ ❡ ❞✐✈❡rt✐♠❡♥t♦ q✉❡ ♠❡ ♣r♦♣♦r❝✐♦♥❛r❛♠✱ s❡♥❞♦ ❡ss❡♥❝✐❛✐s ♣❛r❛ ❡♥❝❛r❛r ❡st❡ ❞❡s❛✜♦ s❡♠♣r❡ ❝♦♠ ❜♦❛ ❞✐s♣♦s✐çã♦✳
❮♥❞✐❝❡
❘❡s✉♠♦ ✐✐✐
❆❜str❛❝t ✈
P❛❧❛✈r❛s ❈❤❛✈❡ ✈✐✐
❑❡②✇♦r❞s ✈✐✐
❆❣r❛❞❡❝✐♠❡♥t♦s ✐①
▲✐st❛ ❞❡ ✜❣✉r❛s ①✈
▲✐st❛ ❞❡ t❛❜❡❧❛s ①✐①
✶ ■♥tr♦❞✉çã♦ ✶
✶✳✶ ▼♦t✐✈❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶ ✶✳✷ ❖❜❥❡❝t✐✈♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷ ✶✳✸ ▼❡t♦❞♦❧♦❣✐❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷ ✶✳✹ ❖r❣❛♥✐③❛çã♦ ❞♦ ❉♦❝✉♠❡♥t♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸ ✷ ❋✉♥❞❛♠❡♥t♦s ❚❡ór✐❝♦s ✺
①✐✈ ❮◆❉■❈❊ ✸✳✹✳✷✳✶ ▼❛❧❤❛s tr✐❛♥❣✉❧❛r❡s ❞❡ s❡✐s ♥ós ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✽ ✸✳✹✳✷✳✷ ▼❛❧❤❛s tr✐❛♥❣✉❧❛r❡s ❞❡ q✉✐♥③❡ ♥ós ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✾ ✸✳✹✳✸ ▼♦❞❡❧❛çã♦ ❡♠ ❙❯❇▲■▼✸❞ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✶ ✸✳✹✳✸✳✶ ▼❛❧❤❛s tr✐❛♥❣✉❧❛r❡s ❞❡ três ♥ós ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✷ ✸✳✹✳✸✳✷ ▼❛❧❤❛s tr✐❛♥❣✉❧❛r❡s ❞❡ s❡✐s ♥ós ✭❚✻✲❊✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✸ ✸✳✹✳✸✳✸ ▼❛❧❤❛s tr✐❛♥❣✉❧❛r❡s ❞❡ s❡✐s ♥ós ✭❚✻✲◆❊✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✹ ✹ ❆♥á❧✐s❡ ❞♦s ❘❡s✉❧t❛❞♦s ✻✺ ✹✳✶ P❧❛❝❛ ❝♦♠ ❢✉r♦ ✭❊P❚✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✺ ✹✳✷ ❱✐❣❛ ❡♠ ❝♦♥s♦❧❛ ✭❊P❚✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✾ ✹✳✸ ❈❛♣❛❝✐❞❛❞❡ ❞❡ ❝❛r❣❛ ❞❡ ❢✉♥❞❛çõ❡s s✉♣❡r✜❝✐❛✐s ✭❊P❉✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✸ ✹✳✹ ❇❧♦❝♦ ❝♦♠ ❡♥t❛❧❤❡s ✭❊P❉✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✺ ✺ ❈♦♥❝❧✉sõ❡s ❡ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦s ❢✉t✉r♦s ✼✾ ✺✳✶ ❉❡s❡♥✈♦❧✈✐♠❡♥t♦s ❢✉t✉r♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✶
▲✐st❛ ❞❡ ❋✐❣✉r❛s
✷✳✶ ❛✮ ▲❡✐ ❞❡ ❡♥❞✉r❡❝✐♠❡♥t♦ ✐s♦tró♣✐❝♦ ❜✮ ▲❡✐ ❞❡ ❡♥❞✉r❡❝✐♠❡♥t♦ ❝✐♥❡♠át✐❝♦ ✭r❡t✐r❛❞♦ ❞❡ ❬✶✸❪✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼ ✷✳✷ ❚✐♣♦s ❞❡ ❊s❝♦❛♠❡♥t♦✿ ❛✮ ❛ss♦❝✐❛❞♦ ❜✮ ♥ã♦ ❛ss♦❝✐❛❞♦ ✭r❡t✐r❛❞♦ ❞❡ ❬✶✸❪✮ ✾ ✷✳✸ ❙✉♣❡r❢í❝✐❡ ❞❡ ❈❡❞ê♥❝✐❛ ❞❡ ❚r❡s❝❛ ❡ ❞❡ ✈♦♥ ▼✐s❡s ✭r❡t✐r❛❞♦ ❞❡ ❬✼❪✮ ✳ ✳ ✳ ✶✵ ✷✳✹ ❙✉♣❡r❢í❝✐❡ ❞❡ ❈❡❞ê♥❝✐❛ ❞❡ ▼♦❤r✲❈♦✉❧♦♠❜ ❡ ❞❡ ❉r✉❝❦❡r✲Pr❛❣❡r ✭r❡t✐⑧
r❛❞♦ ❞❡ ❬✹❪✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷ ✷✳✺ ❛✮ ▲❡✐ ❝♦♥st✐t✉t✐✈❛ ❡❧ást✐❝❛✲❧✐♥❡❛r ❜✮ ▲❡✐ ❝♦♥st✐t✉t✐✈❛ ♥ã♦ ❧✐♥❡❛r ✭❛❞❛♣⑧
t❛❞♦ ❞❡ ❬✶✼❪✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸ ✷✳✻ ❉♦♠í♥✐♦ ❞♦s ❝❛rr❡❣❛♠❡♥t♦s ❛❞♠✐ssí✈❡✐s ✭r❡t✐r❛❞♦ ❞❡ ❬✶✾❪✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✻ ✷✳✼ ❘❡♣r❡s❡♥t❛çã♦ ❣❡♦♠étr✐❝❛ ❞♦ t❡♥s♦r ❞❛s t❡♥sõ❡s ♥♦ ♣❛r❛❧❡❧❡♣í♣❡❞♦
❡❧❡♠❡♥t❛r✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✽ ✷✳✽ ❘❡♣r❡s❡♥t❛çã♦ ❣❡♦♠étr✐❝❛ ❞♦ t❡♥s♦r ❞❛s t❡♥sõ❡s ♥♦ ❡st❛❞♦ ♣❧❛♥♦ ❞❡
t❡♥sã♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✾ ✸✳✶ P❧❛❝❛ ❝♦♠ ❢✉r♦ ❝✐r❝✉❧❛r ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✸ ✸✳✷ ❚r❛♥s❢♦r♠❛çã♦ ❞♦ ❡❧❡♠❡♥t♦ q✉❛❞r❛♥❣✉❧❛r ❡♠ tr✐❛♥❣✉❧❛r ✭r❡t✐r❛❞♦ ❞❡
❬✶❪✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✺ ✸✳✸ ❉✐s❝r❡t✐③❛çã♦ ❞❛ ♣❧❛❝❛ ❝♦♠ ❢✉r♦ ♥♦ s♦❢t✇❛r❡ ❆◆❙❨❙ ✉t✐❧✐③❛♥❞♦ ❡❧❡⑧
①✈✐ ▲■❙❚❆ ❉❊ ❋■●❯❘❆❙ ✸✳✹ ❉✐s❝r❡t✐③❛çã♦ ❞❛ ♣❧❛❝❛ ❝♦♠ ❢✉r♦ ♥♦ s♦❢t✇❛r❡ ❆◆❙❨❙ ✉t✐❧✐③❛♥❞♦ ❡❧❡⑧
♠❡♥t♦s ❚✻✱ ♣❛r❛ ❛s três ♣r✐♠❡✐r❛s ♠❛❧❤❛s ❡st✉❞❛❞❛s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✼ ✸✳✺ ▼❡❝❛♥✐s♠♦ ❞❡ ❝♦❧❛♣s♦ ♣❛r❛ ♦ ♣r♦❜❧❡♠❛ ❞❛ ♣❧❛❝❛ ❝♦♠ ❢✉r♦ ❝✐r❝✉❧❛r ♥♦
s♦❢t✇❛r❡ ❆◆❙❨❙ ✉t✐❧✐③❛♥❞♦ ❡❧❡♠❡♥t♦s ❚✻✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✽ ✸✳✻ ❈❛♠♣♦ ❞❡ t❡♥sõ❡s ♣❛r❛ ♦ ♣r♦❜❧❡♠❛ ❞❛ ♣❧❛❝❛ ❝♦♠ ❢✉r♦ ❝✐r❝✉❧❛r ♥♦
s♦❢t✇❛r❡ ❆◆❙❨❙ ✉t✐❧✐③❛♥❞♦ ❡❧❡♠❡♥t♦s ❚✻✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✽ ✸✳✼ ❉✐ss✐♣❛çã♦ ♣❧ást✐❝❛ ❡ ♠❡❝❛♥✐s♠♦ ❞❡ ❝♦❧❛♣s♦ ♣❛r❛ ♦ ♣r♦❜❧❡♠❛ ❞❛ ♣❧❛❝❛
❝♦♠ ❢✉r♦ ❝✐r❝✉❧❛r ♥♦ s♦❢t✇❛r❡ ❙❯❇▲■▼✸❞ ✉t✐❧✐③❛♥❞♦ ❡❧❡♠❡♥t♦s ❚✸✳ ✳ ✳ ✸✵ ✸✳✽ ❉✐ss✐♣❛çã♦ ♣❧ást✐❝❛ ❡ ♠❡❝❛♥✐s♠♦ ❞❡ ❝♦❧❛♣s♦ ♣❛r❛ ♦ ♣r♦❜❧❡♠❛ ❞❛ ♣❧❛❝❛
❝♦♠ ❢✉r♦ ❝✐r❝✉❧❛r ♥♦ s♦❢t✇❛r❡ ❙❯❇▲■▼✸❞ ✉t✐❧✐③❛♥❞♦ ❡❧❡♠❡♥t♦s ❚✻✳ ✳ ✳ ✸✷ ✸✳✾ ❉✐ss✐♣❛çã♦ ♣❧ást✐❝❛ ❡ ♠❡❝❛♥✐s♠♦ ❞❡ ❝♦❧❛♣s♦ ♣❛r❛ ♦ ♣r♦❜❧❡♠❛ ❞❛ ♣❧❛❝❛
❝♦♠ ❢✉r♦ ❝✐r❝✉❧❛r ♥♦ s♦❢t✇❛r❡ ❙❯❇▲■▼✸❞ ✉t✐❧✐③❛♥❞♦ ❡❧❡♠❡♥t♦s ❚✸✳ ✳ ✳ ✸✸ ✸✳✶✵ ❉✐ss✐♣❛çã♦ ♣❧ást✐❝❛ ❡ ♠❡❝❛♥✐s♠♦ ❞❡ ❝♦❧❛♣s♦ ♣❛r❛ ♦ ♣r♦❜❧❡♠❛ ❞❛ ♣❧❛❝❛
❝♦♠ ❢✉r♦ ❝✐r❝✉❧❛r ♥♦ s♦❢t✇❛r❡ ❙❯❇▲■▼✸❞ ✉t✐❧✐③❛♥❞♦ ❡❧❡♠❡♥t♦s ❚✻✳ ✳ ✳ ✸✹ ✸✳✶✶ ❱✐❣❛ ❡♠ ❝♦♥s♦❧❛ s✉❥❡✐t❛ ❛ ✉♠ ❝❛rr❡❣❛♠❡♥t♦ ❞❡ ❝♦rt❡ ♥❛ s✉❛ ❡①tr❡♠✐⑧
❞❛❞❡ ✭❛❞❛♣t❛❞♦ ❞❡ ❬✶✶❪✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✺ ✸✳✶✷ ❉✐s❝r❡t✐③❛çã♦ ❞❛ ✈✐❣❛ ❡♠ ❝♦♥s♦❧❛ ♥♦ s♦❢t✇❛r❡ ❆◆❙❨❙ ✉t✐❧✐③❛♥❞♦ ❡❧❡⑧
♠❡♥t♦s ❚✸✱ ♣❛r❛ ❛s três ♣r✐♠❡✐r❛s ♠❛❧❤❛s ❡st✉❞❛❞❛s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✼ ✸✳✶✸ ❉✐s❝r❡t✐③❛çã♦ ❞❛ ✈✐❣❛ ❡♠ ❝♦♥s♦❧❛ ♥♦ s♦❢t✇❛r❡ ❆◆❙❨❙ ✉t✐❧✐③❛♥❞♦ ❡❧❡⑧
♠❡♥t♦s ❚✻✱ ♣❛r❛ ❛s três ♣r✐♠❡✐r❛s ♠❛❧❤❛s ❡st✉❞❛❞❛s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✽ ✸✳✶✹ ▼❡❝❛♥✐s♠♦ ❞❡ ❝♦❧❛♣s♦ ♣❛r❛ ♦ ♣r♦❜❧❡♠❛ ❞❛ ✈✐❣❛ ❡♠ ❝♦♥s♦❧❛ ♥♦ s♦❢t✇❛r❡
❆◆❙❨❙ ✉t✐❧✐③❛♥❞♦ ❡❧❡♠❡♥t♦s ❚✻✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✾ ✸✳✶✺ ❈❛♠♣♦ ❞❡ t❡♥sõ❡s ♣❛r❛ ♦ ♣r♦❜❧❡♠❛ ❞❛ ✈✐❣❛ ❡♠ ❝♦♥s♦❧❛ ♥♦ s♦❢t✇❛r❡
❆◆❙❨❙ ✉t✐❧✐③❛♥❞♦ ❡❧❡♠❡♥t♦s ❚✻✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✾ ✸✳✶✻ ❉✐ss✐♣❛çã♦ ♣❧ást✐❝❛ ❡ ♠❡❝❛♥✐s♠♦ ❞❡ ❝♦❧❛♣s♦ ♣❛r❛ ♦ ♣r♦❜❧❡♠❛ ❞❛ ✈✐❣❛
▲■❙❚❆ ❉❊ ❋■●❯❘❆❙ ①✈✐✐ ✸✳✶✽ ❉✐s❝r❡t✐③❛çã♦ ❞❛ s❛♣❛t❛ r❡❝t❛♥❣✉❧❛r ♥♦ s♦❢t✇❛r❡ ❆◆❙❨❙ ✉t✐❧✐③❛♥❞♦
❡❧❡♠❡♥t♦s ❚✻✱ ♣❛r❛ ❛s três ♣r✐♠❡✐r❛s ♠❛❧❤❛s ❡st✉❞❛❞❛s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✺ ✸✳✶✾ ❉✐s❝r❡t✐③❛çã♦ ❞❛ s❛♣❛t❛ r❡❝t❛♥❣✉❧❛r ♥♦ s♦❢t✇❛r❡ P❧❛①✐s ✉t✐❧✐③❛♥❞♦ ❡❧⑧
❡♠❡♥t♦s ❚✻✱ ♣❛r❛ ❛s três ♣r✐♠❡✐r❛s ♠❛❧❤❛s ❡st✉❞❛❞❛s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✽ ✸✳✷✵ ❉✐s❝r❡t✐③❛çã♦ ❞❛ s❛♣❛t❛ r❡❝t❛♥❣✉❧❛r ♥♦ s♦❢t✇❛r❡ P❧❛①✐s ✉t✐❧✐③❛♥❞♦ ❡❧⑧
❡♠❡♥t♦s ❚✶✺✱ ♣❛r❛ ❛s três ♣r✐♠❡✐r❛s ♠❛❧❤❛s ❡st✉❞❛❞❛s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✾ ✸✳✷✶ ▼❡❝❛♥✐s♠♦ ❞❡ ❝♦❧❛♣s♦ ♣❛r❛ ♦ ♣r♦❜❧❡♠❛ ❞❛ s❛♣❛t❛ r❡❝t❛♥❣✉❧❛r ♥♦ s♦❢t⑧
✇❛r❡ P❧❛①✐s ✉t✐❧✐③❛♥❞♦ ❡❧❡♠❡♥t♦s ❚✶✺✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✵ ✸✳✷✷ ❈❛♠♣♦ ❞❡ t❡♥sõ❡s ♣❛r❛ ♦ ♣r♦❜❧❡♠❛ ❞❛ s❛♣❛t❛ r❡❝t❛♥❣✉❧❛r ♥♦ s♦❢t✇❛r❡
P❧❛①✐s ✉t✐❧✐③❛♥❞♦ ❡❧❡♠❡♥t♦s ❚✶✺✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✵ ✸✳✷✸ ❉✐s❝r❡t✐③❛çã♦ ❞❛ s❛♣❛t❛ r❡❝t❛♥❣✉❧❛r ♥♦ s♦❢t✇❛r❡ ❙❯❇▲■▼✸❞ ✉t✐❧✐③❛♥❞♦
❡❧❡♠❡♥t♦s ❚✸✱ ♣❛r❛ ❛s três ♣r✐♠❡✐r❛s ♠❛❧❤❛s ❡st✉❞❛❞❛s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✶ ✸✳✷✹ ❉✐s❝r❡t✐③❛çã♦ ❞❛ s❛♣❛t❛ r❡❝t❛♥❣✉❧❛r ♥♦ s♦❢t✇❛r❡ ❙❯❇▲■▼✸❞ ✉t✐❧✐③❛♥❞♦
❡❧❡♠❡♥t♦s ❚✻✱ ♣❛r❛ ❛s três ♣r✐♠❡✐r❛s ♠❛❧❤❛s ❡st✉❞❛❞❛s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✸ ✸✳✷✺ ❉✐ss✐♣❛çã♦ ♣❧ást✐❝❛ ❡ ♠❡❝❛♥✐s♠♦ ❞❡ ❝♦❧❛♣s♦ ♣❛r❛ ♦ ♣r♦❜❧❡♠❛ ❞❛ s❛♣❛t❛
r❡❝t❛♥❣✉❧❛r ♥♦ s♦❢t✇❛r❡ ❙❯❇▲■▼✸❞ ✉t✐❧✐③❛♥❞♦ ❡❧❡♠❡♥t♦s ❚✻✲◆❊✳ ✳ ✳ ✳ ✺✹ ✸✳✷✻ ❇❧♦❝♦ ❝♦♠ ❡♥t❛❧❤❡s ✭❛❞❛♣t❛❞♦ ❞❡ ❬✶✶❪✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✺ ✸✳✷✼ ❉✐s❝r❡t✐③❛çã♦ ❞♦ ❜❧♦❝♦ ❝♦♠ ❡♥t❛❧❤❡s ♥♦ s♦❢t✇❛r❡ ❆◆❙❨❙ ✉t✐❧✐③❛♥❞♦
❡❧❡♠❡♥t♦s ❚✻✱ ♣❛r❛ ❛s três ♣r✐♠❡✐r❛s ♠❛❧❤❛s ❡st✉❞❛❞❛s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✼ ✸✳✷✽ ❉✐s❝r❡t✐③❛çã♦ ❞♦ ❜❧♦❝♦ ❝♦♠ ❡♥t❛❧❤❡s ♥♦ s♦❢t✇❛r❡ P❧❛①✐s ✉t✐❧✐③❛♥❞♦
❡❧❡♠❡♥t♦s ❚✻✱ ♣❛r❛ ❛s três ♣r✐♠❡✐r❛s ♠❛❧❤❛s ❡st✉❞❛❞❛s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✽ ✸✳✷✾ ❉✐s❝r❡t✐③❛çã♦ ❞♦ ❜❧♦❝♦ ❝♦♠ ❡♥t❛❧❤❡s ♥♦ s♦❢t✇❛r❡ P❧❛①✐s ✉t✐❧✐③❛♥❞♦
❡❧❡♠❡♥t♦s ❚✶✺✱ ♣❛r❛ ❛s três ♣r✐♠❡✐r❛s ♠❛❧❤❛s ❡st✉❞❛❞❛s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✾ ✸✳✸✵ ▼❡❝❛♥✐s♠♦ ❞❡ ❝♦❧❛♣s♦ ♣❛r❛ ♦ ♣r♦❜❧❡♠❛ ❞♦ ❜❧♦❝♦ ❝♦♠ ❡♥t❛❧❤❡s ♥♦
s♦❢t✇❛r❡ P❧❛①✐s ✉t✐❧✐③❛♥❞♦ ❡❧❡♠❡♥t♦s ❚✶✺✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✵ ✸✳✸✶ ❈❛♠♣♦ ❞❡ t❡♥sõ❡s ♣❛r❛ ♦ ♣r♦❜❧❡♠❛ ❞♦ ❜❧♦❝♦ ❝♦♠ ❡♥t❛❧❤❡s ♥♦ s♦❢t✇❛r❡
①✈✐✐✐ ▲■❙❚❆ ❉❊ ❋■●❯❘❆❙ ✸✳✸✷ ❉✐s❝r❡t✐③❛çã♦ ❞♦ ❜❧♦❝♦ ❝♦♠ ❡♥t❛❧❤❡s ♥♦ s♦❢t✇❛r❡ ❙❯❇▲■▼✸❞ ✉t✐❧✐③❛♥❞♦
❡❧❡♠❡♥t♦s ❚✸✱ ♣❛r❛ ❛s três ♣r✐♠❡✐r❛s ♠❛❧❤❛s ❡st✉❞❛❞❛s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✷ ✸✳✸✸ ❉✐s❝r❡t✐③❛çã♦ ❞♦ ❜❧♦❝♦ ❝♦♠ ❡♥t❛❧❤❡s ♥♦ s♦❢t✇❛r❡ ❙❯❇▲■▼✸❞ ✉t✐❧✐③❛♥❞♦
❡❧❡♠❡♥t♦s ❚✻✲❊✱ ♣❛r❛ ❛s três ♣r✐♠❡✐r❛s ♠❛❧❤❛s ❡st✉❞❛❞❛s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✸ ✸✳✸✹ ❉✐ss✐♣❛çã♦ ♣❧ást✐❝❛ ❡ ♠❡❝❛♥✐s♠♦ ❞❡ ❝♦❧❛♣s♦ ♣❛r❛ ♦ ♣r♦❜❧❡♠❛ ❞♦ ❜❧♦❝♦
❝♦♠ ❡♥t❛❧❤❡s ♥♦ s♦❢t✇❛r❡ ❙❯❇▲■▼✸❞ ✉t✐❧✐③❛♥❞♦ ❡❧❡♠❡♥t♦s ❚✻✳ ✳ ✳ ✳ ✳ ✻✹ ✹✳✶ P❧❛❝❛ ❝♦♠ ❢✉r♦✿ ❈♦♥✈❡r❣ê♥❝✐❛ ❞❛ s♦❧✉çã♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✻ ✹✳✷ P❧❛❝❛ ❝♦♠ ❢✉r♦✿ ❚❡♠♣♦ ❞❡ ❝á❧❝✉❧♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✻ ✹✳✸ P❧❛❝❛ ❝♦♠ ❢✉r♦✿ ❈♦♥✈❡r❣ê♥❝✐❛ ❞❛ s♦❧✉çã♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✽ ✹✳✹ P❧❛❝❛ ❝♦♠ ❢✉r♦✿ ❚❡♠♣♦ ❞❡ ❝á❧❝✉❧♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✽ ✹✳✺ ❱✐❣❛ ❡♠ ❝♦♥s♦❧❛✿ ❈♦♥✈❡r❣ê♥❝✐❛ ❞❛ s♦❧✉çã♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✵ ✹✳✻ ❱✐❣❛ ❡♠ ❝♦♥s♦❧❛✿ ❚❡♠♣♦ ❞❡ ❝á❧❝✉❧♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✵ ✹✳✼ ❱✐❣❛ ❡♠ ❝♦♥s♦❧❛✿ ❈♦♠♣❛r❛çã♦ ❞❛ ❝♦♥✈❡r❣ê♥❝✐❛ ❞❛ s♦❧✉çã♦ ♦❜t✐❞❛
▲✐st❛ ❞❡ ❚❛❜❡❧❛s
✸✳✶ ❘❡s✉♠♦ ❞❛s ❛♥á❧✐s❡s ♣❛r❛ ♦ ♣r♦❜❧❡♠❛ ❞❛ ♣❧❛❝❛ ❝♦♠ ❢✉r♦ ❝✐r❝✉❧❛r ♥♦ s♦❢t✇❛r❡ ❆◆❙❨❙ ✉t✐❧✐③❛♥❞♦ ❡❧❡♠❡♥t♦s ❚✸✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✼ ✸✳✷ ❘❡s✉♠♦ ❞❛s ❛♥á❧✐s❡s ♣❛r❛ ♦ ♣r♦❜❧❡♠❛ ❞❛ ♣❧❛❝❛ ❝♦♠ ❢✉r♦ ❝✐r❝✉❧❛r ♥♦
s♦❢t✇❛r❡ ❆◆❙❨❙ ✉t✐❧✐③❛♥❞♦ ❡❧❡♠❡♥t♦s ❚✻✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✽ ✸✳✸ ❘❡s✉♠♦ ❞❛s ❛♥á❧✐s❡s ♣❛r❛ ♦ ♣r♦❜❧❡♠❛ ❞❛ ♣❧❛❝❛ ❝♦♠ ❢✉r♦ ❝✐r❝✉❧❛r ♥♦
s♦❢t✇❛r❡ ❙❯❇▲■▼✸❞ ✉t✐❧✐③❛♥❞♦ ❡❧❡♠❡♥t♦s ❚✸✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✵ ✸✳✹ ❘❡s✉♠♦ ❞❛s ❛♥á❧✐s❡s ♣❛r❛ ♦ ♣r♦❜❧❡♠❛ ❞❛ ♣❧❛❝❛ ❝♦♠ ❢✉r♦ ❝✐r❝✉❧❛r ♥♦
s♦❢t✇❛r❡ ❙❯❇▲■▼✸❞ ✉t✐❧✐③❛♥❞♦ ❡❧❡♠❡♥t♦s ❚✻✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✶ ✸✳✺ ❘❡s✉♠♦ ❞❛s ❛♥á❧✐s❡s ♣❛r❛ ♦ ♣r♦❜❧❡♠❛ ❞❛ ♣❧❛❝❛ ❝♦♠ ❢✉r♦ ❝✐r❝✉❧❛r ♥♦
s♦❢t✇❛r❡ ❙❯❇▲■▼✸❞ ❛tr❛✈és ❞❛ ❛❧t❡r❛çã♦ ❞♦ ♣❛râ♠❡tr♦ ✉t✐❧✐③❛♥❞♦ ❡❧❡♠❡♥t♦s ❚✸✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✸ ✸✳✻ ❘❡s✉♠♦ ❞❛s ❛♥á❧✐s❡s ♣❛r❛ ♦ ♣r♦❜❧❡♠❛ ❞❛ ♣❧❛❝❛ ❝♦♠ ❢✉r♦ ❝✐r❝✉❧❛r ♥♦
s♦❢t✇❛r❡ ❙❯❇▲■▼✸❞ ❛tr❛✈és ❞❛ ❛❧t❡r❛çã♦ ❞♦ ♣❛râ♠❡tr♦ ✉t✐❧✐③❛♥❞♦ ❡❧❡♠❡♥t♦s ❚✻✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✹ ✸✳✼ ❘❡s✉♠♦ ❞❛s ❛♥á❧✐s❡s ♣❛r❛ ♦ ♣r♦❜❧❡♠❛ ❞❛ ✈✐❣❛ ❡♠ ❝♦♥s♦❧❛ ♥♦ s♦❢t✇❛r❡
❆◆❙❨❙ ✉t✐❧✐③❛♥❞♦ ❡❧❡♠❡♥t♦s ❚✸✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✼ ✸✳✽ ❘❡s✉♠♦ ❞❛s ❛♥á❧✐s❡s ♣❛r❛ ♦ ♣r♦❜❧❡♠❛ ❞❛ ✈✐❣❛ ❡♠ ❝♦♥s♦❧❛ ♥♦ s♦❢t✇❛r❡
❆◆❙❨❙ ✉t✐❧✐③❛♥❞♦ ❡❧❡♠❡♥t♦s ❚✻✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✽ ✸✳✾ ❘❡s✉♠♦ ❞❛s ❛♥á❧✐s❡s ♣❛r❛ ♦ ♣r♦❜❧❡♠❛ ❞❛ ✈✐❣❛ ❡♠ ❝♦♥s♦❧❛ ♥♦ s♦❢t✇❛r❡
①① ▲■❙❚❆ ❉❊ ❚❆❇❊▲❆❙ ✸✳✶✵ ❘❡s✉♠♦ ❞❛s ❛♥á❧✐s❡s ♣❛r❛ ♦ ♣r♦❜❧❡♠❛ ❞❛ ✈✐❣❛ ❡♠ ❝♦♥s♦❧❛ ♥♦ s♦❢t✇❛r❡
❙❯❇▲■▼✸❞ ✉t✐❧✐③❛♥❞♦ ❡❧❡♠❡♥t♦s ❚✻✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✶ ✸✳✶✶ ❘❡s✉♠♦ ❞❛s ❛♥á❧✐s❡s ♣❛r❛ ♦ ♣r♦❜❧❡♠❛ ❞❛ s❛♣❛t❛ r❡❝t❛♥❣✉❧❛r ♥♦ s♦❢t⑧
✇❛r❡ ❆◆❙❨❙ ✉t✐❧✐③❛♥❞♦ ❡❧❡♠❡♥t♦s ❚✻✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✻ ✸✳✶✷ ❘❡s✉♠♦ ❞❛s ❛♥á❧✐s❡s ♣❛r❛ ♦ ♣r♦❜❧❡♠❛ ❞❛ s❛♣❛t❛ r❡❝t❛♥❣✉❧❛r ♥♦ s♦❢t⑧
✇❛r❡ P❧❛①✐s ✉t✐❧✐③❛♥❞♦ ❡❧❡♠❡♥t♦s ❚✻✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✽ ✸✳✶✸ ❘❡s✉♠♦ ❞❛s ❛♥á❧✐s❡s ♣❛r❛ ♦ ♣r♦❜❧❡♠❛ ❞❛ s❛♣❛t❛ r❡❝t❛♥❣✉❧❛r ♥♦ s♦❢t⑧
✇❛r❡ P❧❛①✐s ✉t✐❧✐③❛♥❞♦ ❡❧❡♠❡♥t♦s ❚✶✺✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✾ ✸✳✶✹ ❘❡s✉♠♦ ❞❛s ❛♥á❧✐s❡s ♣❛r❛ ♦ ♣r♦❜❧❡♠❛ ❞❛ s❛♣❛t❛ r❡❝t❛♥❣✉❧❛r ♥♦ s♦❢t⑧
✇❛r❡ ❙❯❇▲■▼✸❞ ✉t✐❧✐③❛♥❞♦ ❡❧❡♠❡♥t♦s ❚✸✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✷ ✸✳✶✺ ❘❡s✉♠♦ ❞❛s ❛♥á❧✐s❡s ♣❛r❛ ♦ ♣r♦❜❧❡♠❛ ❞❛ s❛♣❛t❛ r❡❝t❛♥❣✉❧❛r ♥♦ s♦❢t⑧
✇❛r❡ ❙❯❇▲■▼✸❞ ✉t✐❧✐③❛♥❞♦ ❡❧❡♠❡♥t♦s ❚✻✲❊✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✸ ✸✳✶✻ ❘❡s✉♠♦ ❞❛s ❛♥á❧✐s❡s ♣❛r❛ ♦ ♣r♦❜❧❡♠❛ ❞❛ s❛♣❛t❛ r❡❝t❛♥❣✉❧❛r ♥♦ s♦❢t⑧
✇❛r❡ ❆◆❙❨❙ ✉t✐❧✐③❛♥❞♦ ❡❧❡♠❡♥t♦s ❚✻✲◆❊✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✹ ✸✳✶✼ ❘❡s✉♠♦ ❞❛s ❛♥á❧✐s❡s ♣❛r❛ ♦ ♣r♦❜❧❡♠❛ ❞♦ ❜❧♦❝♦ ❝♦♠ ❡♥t❛❧❤❡s ♥♦ s♦❢t⑧
✇❛r❡ ❆◆❙❨❙ ✉t✐❧✐③❛♥❞♦ ❡❧❡♠❡♥t♦s ❚✻✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✼ ✸✳✶✽ ❘❡s✉♠♦ ❞❛s ❛♥á❧✐s❡s ♣❛r❛ ♦ ♣r♦❜❧❡♠❛ ❞♦ ❜❧♦❝♦ ❝♦♠ ❡♥t❛❧❤❡s ♥♦ s♦❢t⑧
✇❛r❡ P❧❛①✐s ✉t✐❧✐③❛♥❞♦ ❡❧❡♠❡♥t♦s ❚✻✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✾ ✸✳✶✾ ❘❡s✉♠♦ ❞❛s ❛♥á❧✐s❡s ♣❛r❛ ♦ ♣r♦❜❧❡♠❛ ❞♦ ❜❧♦❝♦ ❝♦♠ ❡♥t❛❧❤❡s ♥♦ s♦❢t⑧
✇❛r❡ P❧❛①✐s ✉t✐❧✐③❛♥❞♦ ❡❧❡♠❡♥t♦s ❚✶✺✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✵ ✸✳✷✵ ❘❡s✉♠♦ ❞❛s ❛♥á❧✐s❡s ♣❛r❛ ♦ ♣r♦❜❧❡♠❛ ❞♦ ❜❧♦❝♦ ❝♦♠ ❡♥t❛❧❤❡s ♥♦ s♦❢t⑧
✇❛r❡ ❙❯❇▲■▼✸❞ ✉t✐❧✐③❛♥❞♦ ❡❧❡♠❡♥t♦s ❚✸✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✷ ✸✳✷✶ ❘❡s✉♠♦ ❞❛s ❛♥á❧✐s❡s ♣❛r❛ ♦ ♣r♦❜❧❡♠❛ ❞♦ ❜❧♦❝♦ ❝♦♠ ❡♥t❛❧❤❡s ♥♦ s♦❢t⑧
✇❛r❡ ❙❯❇▲■▼✸❞ ✉t✐❧✐③❛♥❞♦ ❡❧❡♠❡♥t♦s ❚✻✲❊✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✸ ✸✳✷✷ ❘❡s✉♠♦ ❞❛s ❛♥á❧✐s❡s ♣❛r❛ ♦ ♣r♦❜❧❡♠❛ ❞♦ ❜❧♦❝♦ ❝♦♠ ❡♥t❛❧❤❡s ♥♦ s♦❢t⑧
❈❛♣ít✉❧♦ ✶
■♥tr♦❞✉çã♦
✶✳✶ ▼♦t✐✈❛çã♦
❆ ❡❧❛❜♦r❛çã♦ ❞❡st❛ t❡s❡ t❡♠ ❝♦♠♦ ♣r✐♥❝✐♣❛❧ ♦❜❥❡❝t✐✈♦ ❛ ♦❜t❡♥çã♦ ❞♦ ❣r❛✉ ❞❡ ▼❡str❡ ❡♠ ❊♥❣❡♥❤❛r✐❛ ❈✐✈✐❧✱ ♥❛ ❋❛❝✉❧❞❛❞❡ ❞❡ ❈✐ê♥❝✐❛s ❡ ❚❡❝♥♦❧♦❣✐❛ ❞❛ ❯♥✐✈❡rs✐❞❛❞❡ ◆♦✈❛ ❞❡ ▲✐s❜♦❛✳ ❆♣❡s❛r ❞❡ ♠❡ s❡♥t✐r ♠❛✐s ✈♦❝❛❝✐♦♥❛❞♦ ♣❛r❛ ❛ ár❡❛ ❞❡ Pr♦❥❡❝t♦ ❞❡ ❊str✉⑧ t✉r❛s ❞❡ ❡♥❣❡♥❤❛r✐❛✱ ❛ ❛♥á❧✐s❡ ♥ã♦ ❧✐♥❡❛r ❞❡ ❡str✉t✉r❛s s❡♠♣r❡ ♠❡ ❞❡s♣❡rt♦✉ ❛❧❣✉♠ ✐♥t❡r❡ss❡✱ ❡s♣❡❝✐❛❧♠❡♥t❡ ✉t✐❧✐③❛♥❞♦ ❢♦r♠✉❧❛çõ❡s ❞❡ ❡❧❡♠❡♥t♦s ✜♥✐t♦s✱ ♠✉✐t♦ ❡♠❜♦r❛ ❢♦ss❡ ✉♠ ❛ss✉♥t♦ ♥♦✈♦ ♣❛r❛ ♠✐♠✳
❖ ❝á❧❝✉❧♦ ❡str✉t✉r❛❧ ❧✐♥❡❛r ❡❧ást✐❝♦ ❛ss✉♠❡✲s❡ ❤♦❥❡ ❡♠ ❞✐❛ ❝♦♠♦ ✉♠❛ ❛❜♦r❞❛❣❡♠ ❜❛st❛♥t❡ s✐♠♣❧❡s ❡ út✐❧✱ ♦ q✉❡ s❡ tr❛❞✉③ ♥♦ ♣r♦❥❡❝t♦ ❞❡ ❡♥❣❡♥❤❛r✐❛ ❡♠ r❡s✉❧t❛❞♦s ❛❝❡✐tá✈❡✐s✳ ❈♦♥t✉❞♦✱ ♦ ❛♣❛r❡❝✐♠❡♥t♦ ❞❡ ♠❡t♦❞♦❧♦❣✐❛s ♠❛t❡♠át✐❝❛s ❛✈❛♥ç❛❞❛s ❛ss♦⑧ ❝✐❛❞❛s ❛♦ tr❛t❛♠❡♥t♦ ❞❡ ❢❡♥ó♠❡♥♦s ❢ís✐❝♦s ❥á ❝♦♥❤❡❝✐❞♦s✱ ✈❡✐♦ tr❛③❡r ♠♦t✐✈❛çã♦ ♣❛r❛ ♦ ❡st✉❞♦ ❞♦ ❝♦♠♣♦rt❛♠❡♥t♦ r❡❛❧ ❞❛s ❡str✉t✉r❛s✱ ✈✐st♦ q✉❡ ❡st❛s ❛♣❡♥❛s s❡ ❝♦♠♣♦rt❛♠✱ ❡✈❡♥t✉❛❧♠❡♥t❡✱ ❞❡ ❢♦r♠❛ ❧✐♥❡❛r ♣❛r❛ ✉♠❛ ❝❡rt❛ ♣❛rt❡ ❞❛s s♦❧✐❝✐t❛çõ❡s s✉♣♦rt❛❞❛s✱ ❞✉r❛♥t❡ ❛ s✉❛ ✈✐❞❛ út✐❧✳ ■st♦ ✈❡r✐✜❝❛✲s❡ ❡s♣❡❝✐❛❧♠❡♥t❡ ❡♠ ❡str✉t✉r❛s q✉❡ ❛♣r❡s❡♥t❡♠ ❡❧❡✈❛❞♦ ❣r❛✉ ❞❡ ❞✉❝t✐❧✐❞❛❞❡ ❡ q✉❛♥❞♦ sã♦ s✉❥❡✐t❛s ❛ ✉♠ t✐♣♦ ❞❡ ❝❛rr❡❣❛♠❡♥t♦ ♥ã♦ ❝í❝❧✐❝♦✳
P♦r ✈❡③❡s✱ é ❛❝♦♥s❡❧❤á✈❡❧ ✉♠❛ ❛♥á❧✐s❡ ♥ã♦ ❧✐♥❡❛r ❞♦ ❝♦♠♣♦rt❛♠❡♥t♦ ❞❡ ❡str✉t✉r❛s ❞❡ ❡❧❡✈❛❞♦ ❣r❛✉ ❞❡ ❝♦♠♣❧❡①✐❞❛❞❡✱ ♣♦✐s ❡♠ ♠✉✐t♦s ❝❛s♦s ❡①✐st❡ ❛ ❝♦♠♣r♦✈❛çã♦✱ ❛tr❛✈és ❞❡ ♠♦❞❡❧♦s ❛♥❛❧ít✐❝♦s ♦✉ r❡s✉❧t❛❞♦ ❞❡ ♦❜s❡r✈❛çõ❡s ❡❢❡❝t✉❛❞❛s✱ q✉❡ ❛ ❛❜♦r❞❛❣❡♠ ✉t✐❧✐③❛❞❛ ♣❛r❛ ❛ r❡s♦❧✉çã♦ ❞♦ ♣r♦❜❧❡♠❛ s❡ ❛❢❛st❛ ❡♠ ♠✉✐t♦ ❞❛ r❡❛❧✐❞❛❞❡✳ ◗✉❡r✲s❡
✷ ❈❆P❮❚❯▲❖ ✶✳ ■◆❚❘❖❉❯➬➹❖ ❝♦♠ ✐st♦ ❞✐③❡r q✉❡ ❛ ♥♦r♠❛❧ ❝♦♥s✐❞❡r❛çã♦ ❞♦s ❞✐❛❣r❛♠❛s ❞❡ ❡s❢♦rç♦s ❡❧ást✐❝♦s ♥♦ ♣r♦❥❡❝t♦ ❞❡ ✉♠❛ ❡str✉t✉r❛ ♣♦❞❡ tr❛❞✉③✐r✲s❡ ♥✉♠ ♠❛✉ r❡s✉❧t❛❞♦✱ ❝❛s♦ s❡ tr❛t❡♠ ❞❡ ❡str✉t✉r❛s ❝♦♠ ✉♠ ❝♦♠♣♦rt❛♠❡♥t♦ ♠❛✐s ❝♦♠♣❧❡①♦✳ ❋♦✐ ❡st❡ ♣♦♥t♦ ❞❡ ✈✐st❛ ❝✐❡♥t✐✜❝♦ q✉❡ ♠❡ ❢❡③ ❞❡s♣❡rt❛r ❝✉r✐♦s✐❞❛❞❡ ♣❡❧♦ t❡♠❛✱ ❛❝✐♠❛ ❞❡ t✉❞♦ ♣♦r s❡r ✉♠ ❛ss✉♥t♦ ♥ã♦ ♠✉✐t♦ ❢❛❧❛❞♦ ❛♦ ❧♦♥❣♦ ❞♦ ❝✉rs♦✱ ♦ q✉❡ ♠❡ ❝♦♠♣❧❡t❛ ♠❛✐s ❡♠ t❡r♠♦s ❞❡ ❝♦♥❤❡❝✐♠❡♥t♦s ❡ ❞❡ ❢♦r♠❛çã♦ ❛❝❛❞é♠✐❝❛✳
✶✳✷ ❖❜❥❡❝t✐✈♦
❖ ♦❜❥❡❝t✐✈♦ ♣r✐♥❝✐♣❛❧ ❞❡st❛ t❡s❡ ❝♦♥s✐st❡ ♥❛ ❞❡t❡r♠✐♥❛çã♦ ❞❡ ❝❛r❣❛s ❞❡ ❝♦❧❛♣s♦ ❞❡ ❡str✉t✉r❛s✱ ❝❛r❛❝t❡r✐③❛❞❛s ♣♦r ✉♠ ❝♦♠♣♦rt❛♠❡♥t♦ ♣❡r❢❡✐t❛♠❡♥t❡ ♣❧ást✐❝♦✱ ❛tr❛✈és ❞❛ ✉t✐❧✐③❛çã♦ ❞❡ ❞♦✐s ♠ét♦❞♦s ❞✐st✐♥t♦s✿ ✉♠ ♣r✐♠❡✐r♦ ♠ét♦❞♦ q✉❡ t❡♠ ❝♦♠♦ ❜❛s❡ ❛ ❞❡⑧ t❡r♠✐♥❛çã♦ ❞❛ ❝❛r❣❛ ú❧t✐♠❛ ❞❡ ✉♠❛ ❡str✉t✉r❛ ❛ ♣❛rt✐r ❞❡ ✉♠❛ ❛♥á❧✐s❡ ❡❧❛st♦✲♣❧ást✐❝❛ ✐♥❝r❡♠❡♥t❛❧ ❡ ✉♠ s❡❣✉♥❞♦ ♠ét♦❞♦ q✉❡ ✈✐s❛ ❞❡t❡r♠✐♥❛r ❡st❛ ♠❡s♠❛ ❝❛r❣❛ ♠❛s ❛❣♦r❛ ✉t✐❧✐③❛♥❞♦ ✉♠❛ ❛♥á❧✐s❡ ❧✐♠✐t❡✱ ♥♦♠❡❛❞❛♠❡♥t❡ ♦ t❡♦r❡♠❛ ❝✐♥❡♠át✐❝♦ ♦✉ t❡♦r❡♠❛ ❞❛ r❡❣✐ã♦ s✉♣❡r✐♦r✳ ❆♣❡s❛r ❞❡ s❡ tr❛t❛r❡♠ ❞❡ ❛❜♦r❞❛❣❡♥s ♣❡r❢❡✐t❛♠❡♥t❡ ❞✐st✐♥t❛s ❡st❛s ❝♦✐♥❝✐❞❡♠ ♥❛ ❜✉s❝❛ ❞♦ ♠❡s♠♦ r❡s✉❧t❛❞♦✱ ♦♥❞❡ é ❢❡✐t♦ ✉♠ ❡st✉❞♦ ❞❛ q✉❛❧✐❞❛❞❡ ❞❛ s♦❧✉çã♦ ♦❜t✐❞❛ ♣❡❧♦s ❞♦✐s ♠ét♦❞♦s ❡ ❛ s✉❛ r❡s♣❡❝t✐✈❛ ❡✜❝✐ê♥❝✐❛✱ tr❛❞✉③✐❞❛ ❡♠ t❡♠♣♦ ❞❡ ❝á❧❝✉❧♦✳
✶✳✸ ▼❡t♦❞♦❧♦❣✐❛
P❛r❛ q✉❡ ❡st❡ ♦❜❥❡❝t✐✈♦ s❡❥❛ ❝✉♠♣r✐❞♦ ❝♦♠ s✉❝❡ss♦✱ ✉t✐❧✐③❛r❛♠✲s❡ três t✐♣♦s ❞❡ s♦❢t⑧ ✇❛r❡s ❞❡ ❡❧❡♠❡♥t♦s ✜♥✐t♦s✱ ❝♦rr❡♥t❡s ♥♦ â♠❜✐t♦ ❞❛ ❡♥❣❡♥❤❛r✐❛ ❝✐✈✐❧✱♥♦♠❡❛❞❛♠❡♥t❡ ♦s s♦❢t✇❛r❡s ❆◆❙❨❙❬✶❪ ❡ P❧❛①✐s❬✷❪ q✉❛♥❞♦ ✐♠♣❧❡♠❡♥t❛❞❛ ✉♠❛ ❛♥á❧✐s❡ ✐♥❝r❡♠❡♥t❛❧ ❞❛ ❝❛r❣❛ ❞❡ ❝♦❧❛♣s♦ ❡ ♦ s♦❢t✇❛r❡ ❙❯❇▲■▼✸❞❬✸❪ q✉❛♥❞♦ ❡st✉❞❛❞❛ ❛ ♠❡s♠❛ ❝❛r❣❛ ❛❣♦r❛ ❛tr❛✈és ❞❡ ✉♠❛ ❛❜♦r❞❛❣❡♠ ❜❛s❡❛❞❛ ♥♦ t❡♦r❡♠❛ ❝✐♥❡♠át✐❝♦ ❞❛ ❛♥á❧✐s❡ ❧✐♠✐t❡✳ ❆ss✐♠✱ ❛♥❛❧✐s❛r❛♠✲s❡ ❞✐✈❡rs♦s ♣r♦❜❧❡♠❛s ✷❉✱ ❡str✉t✉r❛♥❞♦ ✉♠❛ ✐❞❡✐❛ s❡♠❡❧❤❛♥t❡ ♣❛r❛ ❝❛❞❛ ✉♠✿
✶✳✹✳ ❖❘●❆◆■❩❆➬➹❖ ❉❖ ❉❖❈❯▼❊◆❚❖ ✸ ✐✐✳ ■♠♣❧❡♠❡♥t❛çã♦ ❞♦ ♣r♦❜❧❡♠❛ ♥♦ s♦❢t✇❛r❡ ❙❯❇▲■▼✸❞ q✉❛♥❞♦ ❞❡t❡r♠✐♥❛❞❛ ❞❛
❝❛r❣❛ ❞❡ ❝♦❧❛♣s♦ ❞❛ ❡str✉t✉r❛ ❛tr❛✈és ❞❡ ✉♠❛ ❛♥á❧✐s❡ ❧✐♠✐t❡❀
✐✐✐✳ ❈♦♥s✐❞❡r❛çã♦ ❞♦ ❝♦♠♣♦rt❛♠❡♥t♦ ♣❧ást✐❝♦ ❞♦ ♠❛t❡r✐❛❧ ✉t✐❧✐③❛♥❞♦ ♦s ❞♦✐s ♠ét♦⑧ ❞♦s❀
✐✈✳ ❊st✉❞♦ ❞❛ ❡✜❝✐ê♥❝✐❛ ❞♦s ♠ét♦❞♦s ❛tr❛✈és ❞❛ ❛♥á❧✐s❡ ❞♦ t❡♠♣♦ ❞❡ ❝á❧❝✉❧♦ ❞♦ ♣r♦❜❧❡♠❛✳
Pr♦❝❡❞❡✉✲s❡ à ❛♥á❧✐s❡ ❞♦s r❡s✉❧t❛❞♦s ♦❜t✐❞♦s ❛tr❛✈és ❞❛ ❛♣❧✐❝❛çã♦ ❞♦s ❞✐❢❡r❡♥t❡s ♠ét♦❞♦s✱ ♥ã♦ só ❝♦♠♣❛r❛♥❞♦✲♦s ❡♥tr❡ s✐✱ ❡♠ t❡r♠♦s ❞❡ q✉❛❧✐❞❛❞❡ ❞❛ s♦❧✉çã♦ ❞❛ ❝❛r❣❛ ú❧t✐♠❛ ❡ r❡s♣❡❝t✐✈♦ t❡♠♣♦ ❞❡ ❝á❧❝✉❧♦✱ ❝♦♠♦ t❛♠❜é♠ ❝♦♠♣❛r❛♥❞♦✲♦s ❝♦♠ ❡st✉❞♦s ❛♥t❡r✐♦r♠❡♥t❡ r❡❛❧✐③❛❞♦s ♣♦r ♦✉tr♦s ❛✉t♦r❡s✳
✶✳✹ ❖r❣❛♥✐③❛çã♦ ❞♦ ❉♦❝✉♠❡♥t♦
❖ ♣r❡s❡♥t❡ ❞♦❝✉♠❡♥t♦ ❡♥❝♦♥tr❛✲s❡ ❡str✉t✉r❛❞♦ ❡♠ ✺ ❝❛♣ít✉❧♦s✳ P❛r❛ ❛❧é♠ ❞❡st❡ ❝❛♣í⑧ t✉❧♦ ✐♥✐❝✐❛❧ ❞❡ ✐♥tr♦❞✉çã♦✱ ♦♥❞❡ ❢♦✐ ❛♣r❡s❡♥t❛❞❛ ❛ ♠♦t✐✈❛çã♦✱ ♦❜❥❡❝t✐✈♦ ❞♦ tr❛❜❛❧❤♦ ❡ ❛ s✉❛ ♠❡t♦❞♦❧♦❣✐❛✱ ❛♣r❡s❡♥t❛♠✲s❡ ♦s r❡st❛♥t❡s ❝❛♣ít✉❧♦s ❞❡st❛ t❡s❡ ❡ ❛ ❞❡s❝r✐çã♦ s✉♠❛r✐③❛❞❛ ❞♦ s❡✉ ❝♦♥t❡ú❞♦✳
❈❛♣ít✉❧♦ ✷✳ Pr♦❝❡❞❡✲s❡ à ❛♣r❡s❡♥t❛çã♦ ❞❡ ❝♦♥❝❡✐t♦s ❢✉♥❞❛♠❡♥t❛✐s q✉❡ ❢♦r❛♠ t✐❞♦s ❡♠ ❝♦♥t❛ ♥❡st❡ tr❛❜❛❧❤♦✳ ❈♦♠♦ t❛❧✱ sã♦ r❡✈✐st♦s ❛❧❣✉♥s ❝♦♥❝❡✐t♦s ✐♠♣♦rt❛♥t❡s r❡❢❡r❡♥t❡s à ❚❡♦r✐❛ ❞❛ P❧❛st✐❝✐❞❛❞❡✳ ❙ã♦ t❛♠❜é♠ ❛♣r❡s❡♥t❛❞♦s ❝♦♥❝❡✐t♦s ❢✉♥❞❛⑧ ♠❡♥t❛✐s ❞❛ ❆♥á❧✐s❡ ▲✐♠✐t❡ ✐♠♣♦rt❛♥t❡s ♥♦ ❡♥q✉❛❞r❛♠❡♥t♦ t❡ór✐❝♦ ❞❡st❛ t❡s❡✳ P♦r ♦✉tr♦ ❧❛❞♦✱ é ❢❡✐t❛ ✉♠❛ ❜r❡✈❡ ❞❡s❝r✐çã♦ ❞❛s ❡str✉t✉r❛s q✉❛♥❞♦ ♦ s❡✉ ❝♦♠⑧ ♣♦rt❛♠❡♥t♦ ♣♦❞❡ s❡r ❛♥❛❧✐s❛❞♦ s❡❣✉♥❞♦ ✉♠ ❡st❛❞♦ ❞❡ t❡♥sã♦ ♣❧❛♥❛ ♦✉ ❡st❛❞♦ ❞❡ ❞❡❢♦r♠❛çã♦ ♣❧❛♥❛✳
✹ ❈❆P❮❚❯▲❖ ✶✳ ■◆❚❘❖❉❯➬➹❖ ❈❛♣ít✉❧♦ ✹✳ ❖ ♣r✐♥❝✐♣❛❧ ♦❜❥❡❝t✐✈♦ ❞❡st❡ ❝❛♣ít✉❧♦ ❛ss✉♠❡✲s❡ ❝♦♠♦ ❛ ❝♦♠♣❛r❛çã♦ ❞♦s r❡s✉❧t❛❞♦s ♦❜t✐❞♦s ♥♦ ❝❛♣ít✉❧♦ ❛♥t❡r✐♦r✳ ❙❡rá ❛♥❛❧✐s❛❞❛ ❛ q✉❛❧✐❞❛❞❡ ❞❛ s♦❧✉çã♦ ♦❜t✐❞❛ ❡ ❛ r❡s♣❡❝t✐✈❛ ❡✜❝✐ê♥❝✐❛✱ ❝♦♠♣❛r❛♥❞♦✲♦s ❡♥tr❡ s✐ ❡ ❝♦♠ ❡st✉❞♦s r❡❛❧✐③❛❞♦s ♣♦r ♦✉tr♦s ❛✉t♦r❡s✳ ❙ã♦ ❛♣r❡s❡♥t❛❞❛s ❛s ♣r✐♥❝✐♣❛✐s ❝♦♥❝❧✉sõ❡s ❞♦ tr❛❜❛❧❤♦ ❡ sã♦ ❢♦r♥❡❝✐❞❛s ❛s ♣r✐♥❝✐♣❛✐s ❡①♣❧✐❝❛çõ❡s r❡❢❡r❡♥t❡s ❛♦s r❡s✉❧t❛❞♦s ♦❜t✐❞♦s✳
❈❛♣ít✉❧♦ ✷
❋✉♥❞❛♠❡♥t♦s ❚❡ór✐❝♦s
❆ ❞❡t❡r♠✐♥❛çã♦ ❞❡ ❝❛r❣❛s ❞❡ ❝♦❧❛♣s♦ ❛ss✉♠❡ ❤♦❥❡ ❡♠ ❞✐❛ ✉♠ ♣❛♣❡❧ ✐♠♣♦rt❛♥t❡ ♥♦ ❞✐♠❡♥s✐♦♥❛♠❡♥t♦ ❡str✉t✉r❛❧✳ ❖s s♦❢t✇❛r❡s ❞❡ ❡❧❡♠❡♥t♦s ✜♥✐t♦s ✈✐❡r❛♠ tr❛③❡r ✉♠❛ ❡♥♦r♠❡ ❡✈♦❧✉çã♦ ❛ ❡st❡ ❝❛♠♣♦✱ ♣♦✐s ♣♦ss✐❜✐❧✐t❛r❛♠ r❡s♦❧✈❡r ♣r♦❜❧❡♠❛s ❛♥❛❧✐t✐❝❛♠❡♥t❡ ❝♦♠♣❧✐❝❛❞♦s ❝♦♠ ❜❛st❛♥t❡ ❡✜❝á❝✐❛✳ P♦r ♦✉tr♦ ❧❛❞♦✱ ❛ ❝♦♥st❛♥t❡ ❡✈♦❧✉çã♦ t❡❝♥♦❧ó❣✐❝❛ ♣❡r♠✐t❡ ♦ ❛♣❛r❡❝✐♠❡♥t♦ ❞❡ ♥♦✈♦s ❡ ❞✐❢❡r❡♥t❡s t✐♣♦s ❞❡ s♦❢t✇❛r❡s ❞❡ ❞❡t❡r♠✐♥❛çã♦ ❞❡ ❝❛r❣❛s ú❧t✐♠❛s ❞❡ ❡str✉t✉r❛s✳ ❊st❡ tr❛❜❛❧❤♦ s✉r❣❡ ♥❡st❡ ❝♦♥t❡①t♦✱ ♥♦ s❡♥t✐❞♦ ❡♠ q✉❡ s❡rá ❡st✉❞❛❞❛ ❛ q✉❛❧✐❞❛❞❡ ❞❡ ❞♦✐s ♠ét♦❞♦s ❞✐❢❡r❡♥t❡s✱ t❡♥❞♦ ❝♦♠♦ ❜❛s❡✱ ♥❛ ❞❡t❡r♠✐♥❛çã♦ ❞❡ ❝❛r❣❛s ❞❡ ❝♦❧❛♣s♦✱ ❛ ✉t✐❧✐③❛çã♦ ❞❡ s♦❢t✇❛r❡s ❞❡ ❡❧❡♠❡♥t♦s ✜♥✐t♦s✳ ◆❡st❡ ❝❛♣ít✉❧♦ s❡rá ❛♣r❡s❡♥t❛❞♦ ✉♠ ❡♥q✉❛❞r❛♠❡♥t♦ t❡ór✐❝♦ ❞❡st❛ t❡s❡✱ ❝♦♠ ♦ ♦❜❥❡❝⑧ t✐✈♦ ❞❡ ❞❡s❝r❡✈❡r ❞❡ ❢♦r♠❛ ❝♦♠♣❧❡t❛ ♦ ♣r♦❜❧❡♠❛ ❡♠ ❡st✉❞♦✳ P❛r❛ t❛❧✱ s❡rá ❢❡✐t❛ ✉♠❛ r❡✈✐sã♦ ❞❡ ❝♦♥❝❡✐t♦s r❡❧❛❝✐♦♥❛❞♦s ❝♦♠ ❛ ❚❡♦r✐❛ ❞❛ P❧❛st✐❝✐❞❛❞❡ ❬✼❪✱ ❛❜♦r❞❛♥❞♦ t❛♠⑧ ❜é♠ ♦s ❚❡♦r❡♠❛s ❞❛ ❆♥á❧✐s❡ ▲✐♠✐t❡✳ ❙❡rá t❛♠❜é♠ ❡❢❡❝t✉❛❞❛ ✉♠❛ r❡✈✐sã♦ t❡ór✐❝❛ s♦❜r❡ ❛ ❛♥á❧✐s❡ ❡❧❛st♦✲♣❧ást✐❝❛ ✐♥❝r❡♠❡♥t❛❧✳ P♦r ú❧t✐♠♦ s❡rã♦ r❡❝♦r❞❛❞♦s ❛❧❣✉♥s ❝♦♥⑧ ❝❡✐t♦s r❡❧❛❝✐♦♥❛❞♦s ❝♦♠ ♣r♦❜❧❡♠❛s ❜✐❞✐♠❡♥s✐♦♥❛✐s✱ ♥♦♠❡❛❞❛♠❡♥t❡ ❝♦♠♣♦rt❛♠❡♥t♦s ❡♠ ❡st❛❞♦s ♣❧❛♥♦s ❞❡ t❡♥sã♦ ❡ ❡st❛❞♦s ♣❧❛♥♦s ❞❡ ❞❡❢♦r♠❛çã♦✳
❊♠ ♣r✐♠❡✐r♦ ❧✉❣❛r✱ r❡❢❡r❡♠✲s❡ ❛❧❣✉♥s ❝♦♥❝❡✐t♦s ❣❧♦❜❛✐s t✐❞♦s ❡♠ ❝♦♥t❛ ❛♦ ❧♦♥❣♦ ❞❡st❡ ❞♦❝✉♠❡♥t♦✳ ❈♦♥s✐❞❡r♦✉✲s❡ ✈á❧✐❞♦ ♦ ♣r✐♥❝í♣✐♦ ❞❛ ❧✐♥❡❛r✐❞❛❞❡ ❣❡♦♠étr✐❝❛✱ ❣❛r❛♥t✐♥⑧ ❞♦✲s❡ ❛ ❤✐♣ót❡s❡ ❞♦s ♣❡q✉❡♥♦s ❞❡s❧♦❝❛♠❡♥t♦s✳ ❚❡✈❡✲s❡ ❡♠ ❝♦♥s✐❞❡r❛çã♦ q✉❡ t♦❞❛s ❛s ❞❡❢♦r♠❛çõ❡s ❢♦r❛ ❞♦ ❞♦♠í♥✐♦ ❡❧ást✐❝♦ t❡r✐❛♠ ✉♠ ❝♦♠♣♦rt❛♠❡♥t♦ ♣❧ást✐❝♦ ♣❡r❢❡✐t♦ s❡♠ ❡♥❞✉r❡❝✐♠❡♥t♦ ♦✉ ❛♠♦❧❡❝✐♠❡♥t♦✳ ❖s ♠❛t❡r✐❛✐s sã♦ ✐s♦tró♣✐❝♦s ❡ ♥ã♦ ❡①✐st❡♠ ❡❢❡✐t♦s ❞❡ ✐♥ér❝✐❛ ❞❡✈✐❞♦ à ❛♣❧✐❝❛çã♦ ❞♦ ❝❛rr❡❣❛♠❡♥t♦ ❡♠ ❝♦♥❞✐çõ❡s q✉❛s❡ ❡stát✐❝❛s✳
✻ ❈❆P❮❚❯▲❖ ✷✳ ❋❯◆❉❆▼❊◆❚❖❙ ❚❊Ó❘■❈❖❙ ❆❞♠✐t❡✲s❡ ✉♠ ❝♦♠♣♦rt❛♠❡♥t♦ ❞ú❝t✐❧ ❞♦s ♠❛t❡r✐❛✐s✳ ❆ ✐♥❞❡♣❡♥❞ê♥❝✐❛ ❞♦ t❡♠♣♦ ❡ ❞❛ t❡♠♣❡r❛t✉r❛ é t❛♠❜é♠ ❛❞♦♣t❛❞❛✳
✷✳✶ ◆♦çõ❡s ❞❡ P❧❛st✐❝✐❞❛❞❡
❆ ❝❛r❛❝t❡r✐③❛çã♦ ❞♦ ❝♦♠♣♦rt❛♠❡♥t♦ ♣❧ást✐❝♦ ❞❡ ✉♠ ♠❛t❡r✐❛❧ é ❞❡✜♥✐❞❛ ♣❡❧♦ ❡st❛❞♦ ❞❛s t❡♥sõ❡s ❛tr❛✈és ❞♦ s❡✉ ❝r✐tér✐♦ ❞❡ ❝❡❞ê♥❝✐❛✱ q✉❡ ♥❛ s✉❛ ❢♦r♠❛ ♠❛✐s ❣❡r❛❧ s❡ ❛♣r❡s❡♥t❛ ❞♦ s❡❣✉✐♥t❡ ♠♦❞♦✿
f(σ)≤0 ✭✷✳✶✮
❊st❛ ❢♦r♠✉❧❛çã♦ ❡st❛❜❡❧❡❝❡ ✉♠❛ s✉♣❡r❢í❝✐❡ ❞❡ ❝❡❞ê♥❝✐❛✱ f(σ) = 0✱ ❞❡✜♥✐❞❛ ❛tr❛✈és
❞❡ ✉♠❛ ❢✉♥çã♦ ❡s❝❛❧❛r ❞♦ t❡♥s♦r ❞❛s t❡♥sõ❡s✱ q✉❡ r❡♣r❡s❡♥t❛ ♦s ❡st❛❞♦s ❞❡ t❡♥sã♦ ❝♦♥s✐❞❡r❛❞♦s ❛❞♠✐ssí✈❡✐s✳
P❛r❛ q✉❡ ♦❝♦rr❛♠ ❞❡❢♦r♠❛çõ❡s ♣❧ást✐❝❛s ❞♦ ♠❛t❡r✐❛❧ é ♥❡❝❡ssár✐♦ q✉❡ ♦ ❡st❛❞♦ ❞❡ t❡♥sã♦ s❡ ❡♥❝♦♥tr❡ s♦❜r❡ ❛ s✉♣❡r❢í❝✐❡ ❞❡ ❝❡❞ê♥❝✐❛✱ ♦✉ s❡❥❛✱ q✉❡ ❛ ✐❣✉❛❧❞❛❞❡ ♥❛ ❝♦♥❞✐çã♦ ✭✷✳✶✮ s❡❥❛ ✈❡r✐✜❝❛❞❛✳ ❙❡ t❛❧ ♥ã♦ ❛❝♦♥t❡❝❡r ♦ ♠❛t❡r✐❛❧ ❛♣r❡s❡♥t❛✱ ❧♦❝❛❧♠❡♥t❡✱ ✉♠ ❝♦♠♣♦rt❛♠❡♥t♦ ❡♠ r❡❣✐♠❡ ❡❧ást✐❝♦ ♠❛♥t❡♥❞♦✲s❡ ❛s ❞❡❢♦r♠❛çõ❡s ♣❧ást✐❝❛s ❝♦♥st❛♥t❡s✳ ❈♦♥t✉❞♦✱ ♥♦ ❝❛s♦ ♠❛✐s ❣❡♥ér✐❝♦ ♣♦❞❡✲s❡ ❛❞♠✐t✐r q✉❡ ❛ s✉♣❡r❢í❝✐❡ ❞❡ ❝❡❞ê♥❝✐❛ ✐♥✐❝✐❛❧ ♣♦ss❛ s♦❢r❡r ❛❧t❡r❛çõ❡s q✉❛♥❞♦ s❡ ✈❡r✐✜q✉❡♠ ❞❡❢♦r♠❛çõ❡s ♣❧ást✐❝❛s✳ ❊st❡ ❢❡♥ó♠❡♥♦ ❡stá r❡❧❛❝✐♦♥❛❞♦ ❝♦♠ ❛ ❞✐❧❛t❛çã♦ ♦✉ ❝♦♥tr❛❝çã♦ ❞❛ s✉♣❡r❢í❝✐❡ ❞❡ ❝❡❞ê♥❝✐❛✱ ♠❛♥t❡♥❞♦ ❛♣❡s❛r ❞✐st♦ ❛ s✉❛ ❢♦r♠❛ ❡ ♦r✐❣❡♠ ♥♦ ❡s♣❛ç♦ ❞❛s t❡♥sõ❡s✳ ❊st❛ ❞✐❧❛t❛çã♦ ❝♦♥❞✉③ ❛ ✉♠ ❛✉♠❡♥t♦ ❞❡ r❡s✐stê♥❝✐❛ ❞♦ ♠❛t❡r✐❛❧ ❞❡♥♦♠✐♥❛❞♦ ❡♥❞✉r❡❝✐♠❡♥t♦ ✐s♦tró♣✐❝♦ ❬❋✐❣✉r❛ ✷✳✶ ❛✮❪✳ ❆♥❛❧♦❣❛♠❡♥t❡✱ ✈❡r✐✜❝❛✲s❡ q✉❡✱ q✉❛♥❞♦ ❡①✐st❛ ✉♠❛ ❝♦♥tr❛❝çã♦ ❞❛ s✉♣❡r❢í❝✐❡ ❞❡ ❝❡❞ê♥❝✐❛✱ ❡①✐st❡ ✉♠❛ ❞✐♠✐♥✉✐çã♦ ❞❛ r❡s✐stê♥❝✐❛ ❞♦ ♠❛t❡r✐❛❧✱ ❢❡♥ó♠❡♥♦ ❡st❡ ❞❡♥♦♠⑧ ✐♥❛❞♦ ♣♦r ❛♠♦❧❡❝✐♠❡♥t♦✳ P♦❞❡ ❛❝♦♥t❡❝❡r ❡st❛r✲s❡ ♣❡r❛♥t❡ ✉♠ ❝❛s♦ ❞❡ ❛ s✉♣❡r❢í❝✐❡ ❞❡ ❝❡❞ê♥❝✐❛ ✐♥✐❝✐❛❧ ❛♣❡♥❛s s♦❢r❡r tr❛♥s❧❛çõ❡s✱ ♥♦ s❡♥t✐❞♦ ❞❛s ❞❡❢♦r♠❛çõ❡s ♣❧ást✐❝❛s✱ ♠❛♥t❡♥❞♦✲s❡ ✐♥❛❧t❡r❛❞❛ ❛ s✉❛ ❣❡♦♠❡tr✐❛ ✐♥✐❝✐❛❧ ❬❋✐❣✉r❛ ✷✳✶ ❜✮❪✳ ❆ ❡st❡ ❢❡♥ó♠❡♥♦ ❞á✲s❡ ♦ ♥♦♠❡ ❞❡ ❡♥❞✉r❡❝✐♠❡♥t♦ ❝✐♥❡♠át✐❝♦ ❡ é ❝♦♠✉♠ ✉t✐❧✐③❛r✲s❡ q✉❛♥❞♦ s❡ ♣r❡⑧ t❡♥❞❡ ♠♦❞❡❧❛r ❢❡♥ó♠❡♥♦s ❡♠ q✉❡ s❡ ✈❡r✐✜q✉❡ ♦ ❡❢❡✐t♦ ❞❡ ❇❛✉s❝❤✐♥❣❡r❬✼❪✳
❆ss✐♠✱ ❛ s✉♣❡r❢í❝✐❡ ❞❡ ❝❡❞ê♥❝✐❛ ❞❡ ✉♠ ♠❛t❡r✐❛❧ ♥ã♦ ❞❡♣❡♥❞❡ só ❞♦ ❡st❛❞♦ ❞❛s t❡♥sõ❡s✱ ♣❛ss❛♥❞♦ t❛♠❜é♠ ❛ s❡r ❢✉♥çã♦ ❞♦ ❡st❛❞♦ ❞❡ ❡♥❞✉r❡❝✐♠❡♥t♦ ❞♦ ♠❛t❡r✐❛❧✱α✱
✷✳✷✳ ▲❊■ ❉❖ ❊❙❈❖❆▼❊◆❚❖ P▲➪❙❚■❈❖ ✼ ❈♦♥t✉❞♦✱ ♥❡st❡ tr❛❜❛❧❤♦ ❝♦♥s✐❞❡r♦✉✲s❡ q✉❡ ♦ ♠❛t❡r✐❛❧ ❛♣r❡s❡♥t❛✈❛ ✉♠ ❝♦♠♣♦rt❛⑧ ♠❡♥t♦ ♣❡r❢❡✐t❛♠❡♥t❡ ♣❧ást✐❝♦✱ ♦✉ s❡❥❛✱ ❛ ❢✉♥çã♦ft♦r♥❛✲s❡ ✐♥❞❡♣❡♥❞❡♥t❡ ❞❡st❡ ú❧t✐♠♦
♣❛râ♠❡tr♦✱ α = 0✱ ❞❡ ♠❛♥❡✐r❛ q✉❡ ♦s ♣♦♥t♦s ♥♦ ✐♥t❡r✐♦r ❞❛ s✉♣❡r❢í❝✐❡ ♣❡r♠❛♥❡❝❡♠
❡♠ ❡st❛❞♦ ❡❧ást✐❝♦✱ ❡♥q✉❛♥t♦ q✉❡ ♦s ♣♦♥t♦s s♦❜r❡ ❛ s✉♣❡r❢í❝✐❡ s❡ ❡♥❝♦♥tr❛♠ ♥♦ ❡st❛❞♦ ♣❧ást✐❝♦✳
❋✐❣✉r❛ ✷✳✶✿ ❛✮ ▲❡✐ ❞❡ ❡♥❞✉r❡❝✐♠❡♥t♦ ✐s♦tró♣✐❝♦ ❜✮ ▲❡✐ ❞❡ ❡♥❞✉r❡❝✐♠❡♥t♦ ❝✐♥❡♠át✐❝♦ ✭r❡t✐r❛❞♦ ❞❡ ❬✶✸❪✮
✷✳✷ ▲❡✐ ❞♦ ❊s❝♦❛♠❡♥t♦ P❧ást✐❝♦
◆❛ s❡❝çã♦ ❛♥t❡r✐♦r ❢♦r❛♠ ❞❡✜♥✐❞❛s ❛s ❝♦♥❞✐çõ❡s ♥❡❝❡ssár✐❛s ♣❛r❛ ✉♠ ❞❡t❡r♠✐♥❛❞♦ ♠❛⑧ t❡r✐❛❧ ❡♥tr❛r ❡♠ r❡❣✐♠❡ ♣❧ást✐❝♦✳ ❈♦♥t✉❞♦✱ ❛ ♠❛♥❡✐r❛ ❝♦♠♦ s❡ ♣r♦❝❡ss❛ ♦ ❡s❝♦❛♠❡♥t♦ ♥ã♦ ❢♦✐ ❞❡s❝r✐t♦✱ ♦✉ s❡❥❛✱ ♦ q✉❛♥t♦ ❛s ❞❡❢♦r♠❛çõ❡s ♣❧ást✐❝❛s s❡ ❞❡s❡♥✈♦❧✈❡♠ ♣❛r❛ ✉♠ ❞❛❞♦ ❡st❛❞♦ ❞❡ t❡♥sã♦✳ ◆✉♠❛ t❡♦r✐❛ ❞❡ ❡❧❛st♦✲♣❧❛st✐❝✐❞❛❞❡ ❡♥✈♦❧✈❡♥❞♦ ♣❡q✉❡♥❛s ❞❡❢♦r♠❛çõ❡s✱ é ❤❛❜✐t✉❛❧ ❞❡❝♦♠♣♦r✲s❡ ♦ t❡♥s♦r ❞❛s ❞❡❢♦r♠❛çõ❡s ♥✉♠❛ ❝♦♠♣♦♥❡♥t❡ ❡❧ást✐❝❛✱εe✱ ❡ ♥✉♠❛ ❝♦♠♣♦♥❡♥t❡ ♣❧ást✐❝❛✱εp✱ ♣❡r♠✐t✐♥❞♦ q✉❛♥t✐✜❝❛r s❡♣❛r❛❞❛♠❡♥t❡
♦s ❢❡♥ó♠❡♥♦s ❢ís✐❝♦s r❡❧❛❝✐♦♥❛❞♦s ❝♦♠ ❡❧❛st✐❝✐❞❛❞❡ ❡ ♣❧❛st✐❝✐❞❛❞❡✳
ε=εe+εp ✭✷✳✸✮
s❡♥❞♦ q✉❡ ❛ ♣❛r❝❡❧❛εp r❡♣r❡s❡♥t❛ t♦❞❛s ❛s ❞❡❢♦r♠❛çõ❡s ♣❧ást✐❝❛s r❡s✐❞✉❛✐s q✉❡ ♣❡r⑧
♠❛♥❡❝❡♠ ♥♦ ♠❛t❡r✐❛❧ ❛♣ós r❡t✐r❛❞♦ ♦ ❝❛rr❡❣❛♠❡♥t♦✳ ❙❡❣✉♥❞♦ ❛ ❚❡♦r✐❛ ❞❛ ❊❧❛st✐❝✐⑧ ❞❛❞❡✱ ❝♦♥s❡❣✉❡✲s❡ ❡st❛❜❡❧❡❝❡r ✉♠❛ r❡❧❛çã♦ ❡♥tr❡ ❛s ❞❡❢♦r♠❛çõ❡s ❡❧ást✐❝❛s ❡ ♦ ❝❛♠♣♦ ❞❡ t❡♥sõ❡s✱ ❛tr❛✈és ❞❛s ❤❛❜✐t✉❛✐s ❡q✉❛çõ❡s ❝♦♥st✐t✉t✐✈❛s ✭✷✳✹✮✳
✽ ❈❆P❮❚❯▲❖ ✷✳ ❋❯◆❉❆▼❊◆❚❖❙ ❚❊Ó❘■❈❖❙ s❡♥❞♦ q✉❡ Ce r❡♣r❡s❡♥t❛ ♦ t❡♥s♦r ❞❡ q✉❛rt❛ ♦r❞❡♠ q✉❡ ❛r♠❛③❡♥❛ ❛s ❝❛r❛❝t❡ríst✐❝❛s
❡❧ást✐❝❛s ❡ σ ♦ ❝❛♠♣♦ ❞❡ t❡♥sõ❡s✳ ❖ ❝❛♠♣♦ ❞❛s ❞❡❢♦r♠❛çõ❡s ❡❧ást✐❝❛s ❞♦ ♠❛t❡r✐❛❧ é
r❡♣r❡s❡♥t❛❞♦ ♣♦r εe✳
P♦r ♦✉tr♦ ❧❛❞♦✱ t❛❧ ❥á ♥ã♦ s❡ ✈❡r✐✜❝❛ q✉❛♥❞♦ s❡ ❡♥tr❛ ♥♦ r❡❣✐♠❡ ♣❧ást✐❝♦✱ ♦♥❞❡ ❡ss❛s ❧❡✐s ♣❡r❞❡♠ ❢✉♥❞❛♠❡♥t❛çã♦ ❡ ❞❡✐①❛ ❞❡ s❡r ♣♦ssí✈❡❧ ❡st❛❜❡❧❡❝❡r ✉♠❛ r❡❧❛çã♦ ❡♥tr❡ ♦ ❝❛♠♣♦ ❞❡ ❞❡❢♦r♠❛çõ❡s ♣❧ást✐❝❛s ❡ ♦ ❝❛♠♣♦ ❞❡ t❡♥sõ❡s✳ ❆ss✐♠✱ t♦r♥❛✲s❡ ♠❛✐s ❛❞❡q✉❛❞♦ ❡①♣r✐♠✐r ❛ r❡❧❛çã♦ ❝♦♥st✐t✉t✐✈❛ ❛tr❛✈és ❞❡ ✉♠❛ ♥♦✈❛ ❣r❛♥❞❡③❛✱ ❞❡♥♦♠✐♥❛❞❛ t❛①❛ ❞❡ ❞❡❢♦r♠❛çã♦ ♣❧ást✐❝❛✱ε˙p✳
❆ ♣❛rt✐r ❞❡st❛ ❣r❛♥❞❡③❛ s✉r❣❡ ✉♠❛ ♦✉tr❛ ❞❡♥♦♠✐♥❛❞❛ ♣♦t❡♥❝✐❛❧ ♣❧ást✐❝♦✱ Q(σ)✳ ❖
♣♦t❡♥❝✐❛❧ ♣❧ást✐❝♦ é ✉♠❛ ❢✉♥çã♦ ❡s❝❛❧❛r ❞♦ t❡♥s♦r ❞❛s t❡♥sõ❡s ❛ ♣❛rt✐r ❞♦ q✉❛❧ ♦s ✐♥❝r❡♠❡♥t♦s ❞❡ ❞❡❢♦r♠❛çã♦ ♣❧ást✐❝❛ ♣♦❞❡♠ s❡r ❞❡t❡r♠✐♥❛❞♦s ♣♦r ❞❡r✐✈❛çã♦ ♣❛r❝✐❛❧ ❡♠ ♦r❞❡♠ às ❝♦♠♣♦♥❡♥t❡s ❞♦ t❡♥s♦r ❞❛s t❡♥sõ❡s✳ ❊st❡ ♣❡r♠✐t❡ ❡st❛❜❡❧❡❝❡r ✉♠❛ r❡❧❛çã♦ ✐♠♣♦rt❛♥t❡ ❝♦♠ ❛ t❛①❛ ❞❡ ❞❡❢♦r♠❛çã♦ ♣❧ást✐❝❛✳
˙
εp =ξ∂Q(σ)
∂σ , ξ∈R
+
0 ✭✷✳✺✮
❉❡st❡ ♠♦❞♦✱ ❞♦ ♣♦♥t♦ ❞❡ ✈✐st❛ ❣❡♦♠étr✐❝♦✱ ❛ ❝♦♥❞✐çã♦ ✭✷✳✺✮ ❣❛r❛♥t❡ q✉❡ ❛ t❛①❛ ❞❛s ❞❡❢♦r♠❛çõ❡s ♣❧ást✐❝❛s é ♥♦r♠❛❧ à s✉♣❡r❢í❝✐❡ ❞♦ ♣♦t❡♥❝✐❛❧ Q(σ)✳ P♦r ♦✉tr♦ ❧❛❞♦✱ ♦
❡s♣❛ç♦ ❞❡ ✈❛❧♦r❡s ❛ q✉❡ξ ❡stá ❝♦♠♣r❡❡♥❞✐❞♦ ♣❡r♠✐t❡ q✉❡ ♦ s❡♥t✐❞♦ ❞❛s ❞❡❢♦r♠❛çõ❡s
♣❧ást✐❝❛s s❡ ❢❛ç❛ ♣❛r❛ ♦ ❡①t❡r✐♦r ❞❛ ♠❡s♠❛ s✉♣❡r❢í❝✐❡✳ ❉❡st❡ ♠♦❞♦✱ ♣♦❞❡ ❞✐③❡r✲s❡ q✉❡ s❡ ❡stá ♣❡r❛♥t❡ ✉♠❛ ❧❡✐ ❞❡ ❡s❝♦❛♠❡♥t♦ ❛ss♦❝✐❛❞♦✱ q✉❛♥❞♦ s❡ ✈❡r✐✜❝❛ ❛ ✐❣✉❛❧❞❛❞❡
Q(σ) = f(σ)✱ ❝♦♥❢♦r♠❡ s❡ ✐❧✉str❛ ♥❛ ❋✐❣✉r❛ ✷✳✷✳ ◆❡st❡ tr❛❜❛❧❤♦✱ ✉t✐❧✐③♦✉✲s❡ ✉♠❛ ❧❡✐
❞❡ ✢✉①♦ ❛ss♦❝✐❛❞❛✱ ❣❛r❛♥t✐♥❞♦ ❛ss✐♠ q✉❡ ❛ ❝♦♥❞✐çã♦ ❞❡ ♥♦r♠❛❧✐❞❛❞❡ ❢♦ss❡ ✈❡r✐✜❝❛❞❛ ❡♠ q✉❛❧q✉❡r ♣♦♥t♦ ❞♦ ❡s♣❛ç♦ ❞❡ t❡♥sõ❡s✱✳
✷✳✸✳ ❈❘■❚➱❘■❖❙ ❉❊ ❈❊❉✃◆❈■❆ ✾
❋✐❣✉r❛ ✷✳✷✿ ❚✐♣♦s ❞❡ ❊s❝♦❛♠❡♥t♦✿ ❛✮ ❛ss♦❝✐❛❞♦ ❜✮ ♥ã♦ ❛ss♦❝✐❛❞♦ ✭r❡t✐r❛❞♦ ❞❡ ❬✶✸❪✮
✷✳✸ ❈r✐tér✐♦s ❞❡ ❈❡❞ê♥❝✐❛
◆❡st❛ s❡❝çã♦ s❡rã♦ ❛♣r❡s❡♥t❛❞♦s ♦s q✉❛tr♦ ❝r✐tér✐♦s ❞❡ ❝❡❞ê♥❝✐❛ ♠❛✐s ❝♦♠✉♥s✳ ❙❡rá ❡❢❡❝t✉❛❞❛ ✉♠❛ ❜r❡✈❡ ❞❡s❝r✐çã♦ s♦❜r❡ ❝❛❞❛ ✉♠ ❞❡❧❡s✱ ❞❡s❝r✐çã♦ ❡st❛ ❛❝♦♠♣❛♥❤❛❞❛ ♣❡❧❛ r❡♣r❡s❡♥t❛çã♦ ❣rá✜❝❛ ❞❛s r❡s♣❡❝t✐✈❛s s✉♣❡r❢í❝✐❡s ❞❡ ❝❡❞ê♥❝✐❛✳
✷✳✸✳✶ ❈r✐tér✐♦ ❞❡ ✈♦♥ ▼✐s❡s
❖ ❝r✐tér✐♦ ❞❡ ✈♦♥ ▼✐s❡s ❞❡✜♥❡ q✉❡ ✉♠ ❞❡t❡r♠✐♥❛❞♦ ♠❛t❡r✐❛❧ ❡♥tr❛ ❡♠ ❝❡❞ê♥❝✐❛ q✉❛♥❞♦ ❛ s❡❣✉✐♥t❡ ❝♦♥❞✐çã♦ ❞❡✐①❛ ❞❡ s❡r ✈❡r✐✜❝❛❞❛✿
1
2[(σI −σII) 2
+ (σII −σIII)
2
+ (σIII −σI)
2
]6Y2 ✭✷✳✻✮
♦♥❞❡Y =√3k✱ ❡♠ q✉❡ ❦ r❡♣r❡s❡♥t❛ ❛ t❡♥sã♦ ❞❡ ❝♦rt❡ ❞❡ ❝❡❞ê♥❝✐❛ ♦❜t✐❞❛ ♥✉♠ ❡♥s❛✐♦
❞❡ tr❛❝çã♦ ✉♥✐❛①✐❛❧✳
P♦r ♦✉tr♦ ❧❛❞♦✱ ♦ â♠❜✐t♦ ❞♦s ❡st✉❞♦s ❡❢❡❝t✉❛❞♦s ♥❡st❛ ❞✐ss❡rt❛çã♦ ✐♥s❡r❡♠✲s❡ s♦❜r❡ ❝❛s♦s ♣❧❛♥♦s ❞❡ t❡♥sã♦✱ ♣♦❞❡♥❞♦ ❛ ❡①♣r❡ssã♦ ✭✷✳✻✮ s❡r r❡❞✉③✐❞❛ ❛♦ s❡❣✉✐♥t❡✿
σ2
I −σIσII+σ
2
II ≤Y
✶✵ ❈❆P❮❚❯▲❖ ✷✳ ❋❯◆❉❆▼❊◆❚❖❙ ❚❊Ó❘■❈❖❙
✷✳✸✳✷ ❈r✐tér✐♦ ❞❡ ❚r❡s❝❛
❆ ❢✉♥çã♦ q✉❡ ❞❡✜♥❡ ❛ s✉♣❡r❢í❝✐❡ ❞❡ ❝❡❞ê♥❝✐❛ ❞❡ ❚r❡s❝❛ é ❞❛❞❛ ♣❡❧❛ s❡❣✉✐♥t❡ ❡①♣r❡ssã♦✿
f(σ) =σI −σIII −2c ✭✷✳✽✮
♦♥❞❡✱ cr❡♣r❡s❡♥t❛ ❛ ❝♦❡sã♦ ❞♦ ♠❛t❡r✐❛❧✳
❋✐❣✉r❛ ✷✳✸✿ ❙✉♣❡r❢í❝✐❡ ❞❡ ❈❡❞ê♥❝✐❛ ❞❡ ❚r❡s❝❛ ❡ ❞❡ ✈♦♥ ▼✐s❡s ✭r❡t✐r❛❞♦ ❞❡ ❬✼❪✮ ❖ ❝r✐tér✐♦ ❞❡ ❝❡❞ê♥❝✐❛ ❞❡ ❚r❡s❝❛ ♥✉♠ ❡st❛❞♦ ♣❧❛♥♦ ❞❡ t❡♥sã♦ ✭σIII = 0✮✶✱ r❡♣r❡s❡♥⑧
t❛❞♦ ♥❛ ❋✐❣✉r❛ ✷✳✸✱ ♣♦❞❡ s❡r ❞❡❧✐♠✐t❛❞♦ ♣❡❧❛s s❡❣✉✐♥t❡s ❧✐♥❤❛s r❡❝t❛s✿
σI =±Y σII =±Y σI −σII =±Y ✭✷✳✾✮
❖❜s❡r✈❡ ♦ ❧❡✐t♦r ❛ ♣❧❛♥✐✜❝❛çã♦ ❞❛ ❡❧✐♣s❡ ❞❡ ✈♦♥ ▼✐s❡s ❡ ♦ ❤❡①á❣♦♥♦ ❞❡ ❚r❡s❝❛ ❛♣r❡⑧ s❡♥t❛❞♦s ♥❛ ❋✐❣✉r❛ ✷✳✸✳ ❱❡r✐✜q✉❡ q✉❡ ❛ ❡❧✐♣s❡ ❞❡ ▼✐s❡s ❝✐r❝✉♥s❝r❡✈❡ ♦ ❤❡①á❣♦♥♦ ❞❡ ❚r❡s❝❛ ♣❛r❛ ✉♠❛ t❡♥sã♦ ❞❡ ❝❡❞ê♥❝✐❛ ✉♥✐❛①✐❛❧ ❨✱ ♣♦❞❡♥❞♦ ❛✜r♠❛r✲s❡ q✉❡ ♦ ❝r✐tér✐♦ ❞❡ ❚r❡s❝❛ é ❞❡ ❡♥tr❡ ❡❧❡s ♦ ♠❛✐s ❝♦♥s❡r✈❛t✐✈♦✱ ♣♦✐s ❡st❡ ❡♥❝♦♥tr❛✲s❡ ❡♥✈♦❧✈✐❞♦ ♣❡❧❛ ❡❧✐♣s❡ ❞❡ ✈♦♥ ▼✐s❡s✳
✷✳✸✳ ❈❘■❚➱❘■❖❙ ❉❊ ❈❊❉✃◆❈■❆ ✶✶
✷✳✸✳✸ ❈r✐tér✐♦ ❞❡ ▼♦❤r✲❈♦✉❧♦♠❜
❖ ❝r✐tér✐♦ ❞❡ ❝❡❞ê♥❝✐❛ ❞❡ ▼♦❤r✲❈♦✉❧♦♠❜ é ♥♦r♠❛❧♠❡♥t❡ ✉t✐❧✐③❛❞♦ ♣❛r❛ ♠♦❞❡❧❛r ♦ ❝♦♠♣♦rt❛♠❡♥t♦ ❞❡ ♠❛t❡r✐❛✐s ❣r❛♥✉❧❛r❡s✳ ❊st❡ ♣♦❞❡ s❡r ❞❡✜♥✐❞♦ ♣❡❧❛ s❡❣✉✐♥t❡ ❡①♣r❡ssã♦✿
f(σ) = σI(1 + sinφ)−σIII(1−sinφ)−2ccosφ ✭✷✳✶✵✮
♦♥❞❡φ r❡♣r❡s❡♥t❛ ♦ â♥❣✉❧♦ ❞❡ ❛tr✐t♦ ✐♥t❡r♥♦ ❞♦ ♠❛t❡r✐❛❧✳
➱ ✐♥t❡r❡ss❛♥t❡ ✈❡r✐✜❝❛r q✉❡ ♥♦ ❝❛s♦ ❞❡ ♦ â♥❣✉❧♦ ❞❡ ❛tr✐t♦ ✐♥t❡r♥♦ s❡r ♥✉❧♦✱ φ = 0✱
❛ s✉♣❡r❢í❝✐❡ ❞❡ ❝❡❞ê♥❝✐❛ ❞❡ ▼♦❤r✲❈♦✉❧♦♠❜ ❞❡✐①❛ ❞❡ s❡r ✉♠❛ ♣✐râ♠✐❞❡ ❤❡①❛❣♦♥❛❧✱ ♣❛ss❛♥❞♦ ❛ s❡r ✉♠ ♣r✐s♠❛ ❞❡ ✐❣✉❛❧ ❜❛s❡✱ ♦ q✉❡ s✐❣♥✐✜❝❛ q✉❡ q✉❛♥❞♦ t❛❧ ❛❝♦♥t❡❝❡✱ ❡st❡ ❝r✐tér✐♦ ❝♦✐♥❝✐❞❡ ❝♦♠ ♦ ❝r✐tér✐♦ ❞❡ ❚r❡s❝❛✳ ◆❡st❡ ❝❛s♦✱ ❛ s✉♣❡r❢í❝✐❡ ❞❡ ❝❡❞ê♥❝✐❛ ♣❛ss❛ ❛ s❡r r❡♣r❡s❡♥t❛❞❛ ♣❡❧❛ s❡❣✉✐♥t❡ ❡①♣r❡ssã♦ ✭✷✳✽✮
✷✳✸✳✹ ❈r✐tér✐♦ ❞❡ ❉r✉❝❦❡r✲Pr❛❣❡r
P♦r ú❧t✐♠♦ ❛♣r❡s❡♥t❛✲s❡ ♦ ❝r✐tér✐♦ ❞❡ ❉r✉❝❦❡r✲Pr❛❣❡r✳ ❆ ❡①♣r❡ssã♦ q✉❡ ❞❡✜♥❡ ❛ s✉❛ s✉♣❡r❢í❝✐❡ ❞❡ ❝❡❞ê♥❝✐❛ é ❛♣r❡s❡♥t❛❞❛ ❛❜❛✐①♦ ❡ ♣♦❞❡ s❡r ✈✐s✉❛❧✐③❛❞❛ ♥❛ ❋✐❣✉r❛ ✷✳✹✳
f(σ) = 3ασm+ p
J2−k ′
✭✷✳✶✶✮ ❡♠ q✉❡ ♦s ❝♦❡✜❝✐❡♥t❡s α ❡ k′
sã♦ ❝♦♥st❛♥t❡s ❞♦ ♠❛t❡r✐❛❧ ❡ ❞❡♣❡♥❞❡♠ ❞♦ â♥❣✉❧♦ ❞❡ ❛tr✐t♦ ✐♥t❡r♥♦ ✭φ✮ ❡ ❞❛ ❝♦❡sã♦ ✭c✮ ❡ σm r❡♣r❡s❡♥t❛ ❛ t❡♥sã♦ ♠é❞✐❛✿
k′ = √ 6c×cosφ
3×(3−sinφ) ✭✷✳✶✷✮
α= √ 2 sinφ
3×(3−sinφ) ✭✷✳✶✸✮
σm =
1
3(σx+σy+σx) ✭✷✳✶✹✮
❆❝r❡s❝❡♥t❛✲s❡ q✉❡ J2✱ ✭✷✳✶✺✮✱ r❡♣r❡s❡♥t❛ ♦ s✐♠étr✐❝♦ ❞♦ s❡❣✉♥❞♦ ✐♥✈❛r✐❛♥t❡ ❞❛s t❡♥⑧
✶✷ ❈❆P❮❚❯▲❖ ✷✳ ❋❯◆❉❆▼❊◆❚❖❙ ❚❊Ó❘■❈❖❙ ❝❡❞ê♥❝✐❛ ❞❡ ❉r✉❝❦❡r✲Pr❛❣❡r ❞❡✐①❛ ❞❡ s❡r ❝ó♥✐❝❛✱ ♣❛ss❛♥❞♦ ❛ ❝♦✐♥❝✐❞✐r ❝♦♠ ♦ ❝✐❧✐♥❞r♦ ❞❡ ✈♦♥ ▼✐s❡s✱ ❝♦♠♦ ♠♦str❛ ❛ ❋✐❣✉r❛ ✷✳✹✳
J2 = 1
2[(σx−σm) 2
+ (σy −σm)
2
+ (σz−σm)
2 ] +σ2
xy +σ
2
xz+σ
2
yz ✭✷✳✶✺✮
❆✐♥❞❛ ❡♠ r❡❧❛çã♦ ❛♦ s✐♠étr✐❝♦ ❞♦ s❡❣✉♥❞♦ ✐♥✈❛r✐❛♥t❡ ❞❛s t❡♥sõ❡s ❞❡ ❞❡s✈✐♦✱ J2✱ ♦
❝r✐tér✐♦ ❞❡ ❝❡❞ê♥❝✐❛ ❞❡ ❞❡ ✈♦♥ ▼✐s❡s s✉❣❡r❡ q✉❡ ✉♠ ❞❛❞♦ ♠❛t❡r✐❛❧ ❡♥tr❛ ❡♠ ❝❡❞ê♥❝✐❛ q✉❛♥❞♦ ❡st❡ ✐♥✈❛r✐❛♥t❡ ❛t✐♥❣❡ ♦ s❡✉ ✈❛❧♦r ❝rít✐❝♦✳ ❈♦♠♦ t❛❧✱ ♦ ❝r✐tér✐♦ ❞❡ ✈♦♥ ▼✐s❡s ♣♦❞❡ s❡r ❡①♣r❡ss♦ ❡♠ ❢✉♥çã♦ ❞❡ J2✱ ❛tr❛✈és ❞❛ r❡❧❛çã♦ ✭✷✳✶✻✮✳
Y =pJ2−k ✭✷✳✶✻✮
❡♠ q✉❡ ❦ r❡♣r❡s❡♥t❛✱ ❝♦♠♦ ❢♦✐ r❡❢❡r✐❞♦ ❛♥t❡r✐♦r♠❡♥t❡ ❡♠ ✭✷✳✻✮✱ ❛ t❡♥sã♦ ❞❡ ❝♦rt❡ ❞❡ ❝❡❞ê♥❝✐❛ ♦❜t✐❞❛ ♥✉♠ ❡♥s❛✐♦ ❞❡ tr❛❝çã♦ ✉♥✐❛①✐❛❧✳
❋✐❣✉r❛ ✷✳✹✿ ❙✉♣❡r❢í❝✐❡ ❞❡ ❈❡❞ê♥❝✐❛ ❞❡ ▼♦❤r✲❈♦✉❧♦♠❜ ❡ ❞❡ ❉r✉❝❦❡r✲Pr❛❣❡r ✭r❡t✐r❛❞♦ ❞❡ ❬✹❪✮
✷✳✹ ❆♥á❧✐s❡ ❡❧❛st♦✲♣❧ást✐❝❛ ✐♥❝r❡♠❡♥t❛❧
✷✳✹✳ ❆◆➪▲■❙❊ ❊▲❆❙❚❖✲P▲➪❙❚■❈❆ ■◆❈❘❊▼❊◆❚❆▲ ✶✸ q✉❡ ❤❛❥❛ ♦❝♦rrê♥❝✐❛ ❞♦ ❝♦❧❛♣s♦ ❞❛ ❡str✉t✉r❛✳
❈♦♠♦ ❢♦✐ r❡❢❡r✐❞♦ ❛♥t❡r✐♦r♠❡♥t❡✱ q✉❛♥❞♦ s❡ ❡♥tr❛ ♥♦ ❝❛♠♣♦ ❞❛ ♣❧❛st✐❝✐❞❛❞❡✱ ❛s ❧❡✐s ❝♦♥st✐t✉t✐✈❛s q✉❡ ♣❡r♠✐t✐❛♠ ❞❡✜♥✐r ♦ ♣r♦❜❧❡♠❛ ❡♠ r❡❣✐♠❡ ❡❧ást✐❝♦ ❞❡✐①❛♠ ❞❡ s❡r ✈á❧✐❞❛s✳ ◆❡st❡ ❝❛s♦✱ ❝♦♥s✐❞❡r❛♥❞♦ ✉♠ ♠❛t❡r✐❛❧ ❡❧❛st♦✲♣❧ást✐❝♦✱ ❛s ❧❡✐s ❛ ❛♣❧✐❝❛r sã♦ ♥ã♦ ❧✐♥❡❛r❡s✱ ♣♦✐s ♦ t❡♥s♦r q✉❡ r❡❧❛❝✐♦♥❛ ❛ t❡♥sã♦ ❝♦♠ ❛ ❞❡❢♦r♠❛çã♦ é ❢✉♥çã♦ ❞♦ ❡st❛❞♦ ❞❡ t❡♥sõ❡s✳ ❚❡♥❞♦ ❝♦♠♦ ❜❛s❡ ❡st❡ ❛s♣❡❝t♦✱ ❛ r❡❧❛çã♦ ❝♦♥st✐t✉t✐✈❛ ❞❡✈❡ s❡r ❞❡✜♥✐❞❛ ❡st❛❜❡❧❡❝❡♥❞♦ ✉♠❛ r❡❧❛çã♦ ❡♥tr❡ ✐♥❝r❡♠❡♥t♦s ❞❡ t❡♥sõ❡s ❡ ✐♥❝r❡♠❡♥t♦s ❞❡ ❞❡❢♦r♠❛çõ❡s✱ ❝♦♠♦ ♠♦str❛ ❛ ❋✐❣✉r❛ ✷✳✺✳
❋✐❣✉r❛ ✷✳✺✿ ❛✮ ▲❡✐ ❝♦♥st✐t✉t✐✈❛ ❡❧ást✐❝❛✲❧✐♥❡❛r ❜✮ ▲❡✐ ❝♦♥st✐t✉t✐✈❛ ♥ã♦ ❧✐♥❡❛r ✭❛❞❛♣t❛❞♦ ❞❡ ❬✶✼❪✮
❙❡DN L =f(σ)❢♦r ❛ r❡♣r❡s❡♥t❛çã♦ t❡♥s♦r✐❛❧ ❞❡ ✉♠ ❞❛❞❛ ❧❡✐ ❝♦♥st✐t✉t✐✈❛ ♥ã♦ ❧✐♥❡❛r ❡ CN L =g(σ)❢♦r ♦ s❡✉ ✐♥✈❡rs♦✱ ❛s r❡❧❛çõ❡s ❡♥tr❡ ✐♥❝r❡♠❡♥t♦s ❞❡ t❡♥sã♦ ❡ ✐♥❝r❡♠❡♥t♦s
❞❡ ❞❡❢♦r♠❛çã♦ ♣♦❞❡♠ s❡r ❞❡s❝r✐t❛s ♣❡❧❛s ❡q✉❛çõ❡s ✭✷✳✶✼✮ ❡ ✭✷✳✶✽✮✳
dσ =CN L(σ) :dε ✭✷✳✶✼✮ dε=DN L(σ) :dσ ✭✷✳✶✽✮
✶✹ ❈❆P❮❚❯▲❖ ✷✳ ❋❯◆❉❆▼❊◆❚❖❙ ❚❊Ó❘■❈❖❙ s✉❛ ❢♦r♠❛ ♠❛✐s s✐♠♣❧❡s ❝♦♠♦ ♠ét♦❞♦s ❧✐♥❡❛r❡s q✉❡ r❡s✉❧t❛♠ ❞❛ ❝♦♥❥✉❣❛çã♦ ❞❡ ✈ár✐♦s ♣❛ss♦s ❞❡ ❝❛r❣❛✱ ✈❛r✐❛♥❞♦ ❝♦♥s♦❛♥t❡ ❛ r❡s♣♦st❛ ❛♦ ú❧t✐♠♦ ❝❛rr❡❣❛♠❡♥t♦ ❛♣❧✐❝❛❞♦✱ ♦✉ s❡❥❛✱ ❡st❛♥❞♦ ♦✉ ♥ã♦ ❡♠ r❡❣✐♠❡ ♣❧ást✐❝♦✳
◆ã♦ q✉❡r❡♥❞♦ ❛♣r♦❢✉♥❞❛r ♠✉✐t♦ ❡st❡ t❡♠❛✱ ❞❡st❛❝❛♠✲s❡ ❛❧❣✉♥s ❛✉t♦r❡s q✉❡ ♣❡r♠✐t✐⑧ r❛♠ ❛ ❡✈♦❧✉çã♦ ❞❡st❡ ♣r♦❝❡ss♦ ✐♥❝r❡♠❡♥t❛❧ ♥♦ â♠❜✐t♦ ❞❡ ♠♦❞❡❧♦s ❞❡ ❡❧❡♠❡♥t♦s ✜♥✐⑧ t♦s✳ ❯♠ ❞♦s ♣r✐♠❡✐r♦s ♣r♦❝❡ss♦s ✉t✐❧✐③❛❞♦s ❢♦✐ ❞❡s❡♥✈♦❧✈✐❞♦ ♣♦r ●❡❛r ❬✾❪✱ ❡♠ ✶✾✼✶✱ q✉❡ ❝♦♥s✐st✐❛ ♥❛ ❛♣❧✐❝❛çã♦ ❞❡st❡s ♣r❡ss✉♣♦st♦s ❛tr❛✈és ❞❛ ✉t✐❧✐③❛çã♦ ❞❡ s✐st❡♠❛s ❛❧⑧ ❣é❜r✐❝♦s ❞❡ ❡q✉❛çõ❡s ❞✐❢❡r❡♥❝✐❛✐s✳ ❖✉tr♦s ❛✉t♦r❡s ❢♦r❛♠ ❞❡s❡♥✈♦❧✈❡♥❞♦ ❛❧❣♦r✐t♠♦s ♥❡st❛ ár❡❛✱ s❡♥❞♦ ❤♦❥❡ ❡♠ ❞✐❛ ♦ ❡sq✉❡♠❛ ❞❡ ✐♥t❡❣r❛çã♦ ◆❡✇t♦♥✲❘❛♣❤s♦♥ ♦ ♠❛✐s ✉t✐❧✐③❛❞♦ ❡♠ s♦❢t✇❛r❡s ❞❡ ❡❧❡♠❡♥t♦s ✜♥✐t♦s ♣❛r❛ ❞❡t❡r♠✐♥❛r ♥♦✈♦s ❡st❛❞♦s ❞❡ t❡♥sã♦ ♦✉ ❞❡❢♦r♠❛çã♦✱ ❛❝t✉❛❧✐③❛♥❞♦ ♦ t❛♠❛♥❤♦ ❞❛ s✉♣❡r❢í❝✐❡ ❞❡ ♣❧❛st✐✜❝❛çã♦ ✭❙❧♦❛♥ ❬✷✵❪✮✳ ❈♦♠♦ s❡ tr❛t❛ ❞❡ ✉♠ ♠ét♦❞♦ ❞❡ ♣r✐♠❡✐r❛ ♦r❞❡♠✱ ❛ q✉❛❧✐❞❛❞❡ ❞♦ r❡s✉❧t❛❞♦ ❞❛ ✐♥t❡⑧ ❣r❛çã♦ ♥✉♠ér✐❝❛ só s❡rá ❛❞❡q✉❛❞❛ s❡ ♦s ✐♥❝r❡♠❡♥t♦s ❞❡ ❞❡❢♦r♠❛çã♦ ❢♦r❡♠ ♣❡q✉❡♥♦s✳ ❊st❡ ❡sq✉❡♠❛ ✉t✐❧✐③❛ ❛s ♣r✐♠❡✐r❛s ❞❡r✐✈❛❞❛s ❞❛ ❢✉♥çã♦ ❞❡ ♣♦t❡♥❝✐❛❧ ♣❧ást✐❝♦ ✭✷✳✺✮✳ ▼❛✐s t❛r❞❡ ❡st❡s ❛❧❣♦r✐t♠♦s ❢♦r❛♠ ❛♣❧✐❝❛❞♦s à ✐♥t❡❣r❛çã♦ ❞❛s r❡❧❛çõ❡s ❡❧❛st♦✲♣❧ás⑧ t✐❝❛s q✉❡ ✉t✐❧✐③❛♠ ♦s ❝r✐tér✐♦s ❞❡ ❝❡❞ê♥❝✐❛✱ ❛♥t❡r✐♦r♠❡♥t❡ r❡❢❡r✐❞♦s ♥❛ s❡❝çã♦ ✷✳✸✱ s❡♥❞♦ ♣♦rt❛♥t♦ ♦s ❛♣❧✐❝❛❞♦s ♥❡st❡ tr❛❜❛❧❤♦ ❛tr❛✈és ❞❛ ✉t✐❧✐③❛çã♦ ❞♦s s♦❢t✇❛r❡s✱ ❞❡ ❛♥á❧✐s❡ ❡❧❛st♦✲♣❧ást✐❝❛✱ ❆◆❙❨❙ ❡ P❧❛①✐s✳
