O caso de problemas de contato mecânico é um caso bastante amplo com diversos problemas de interesse na engenharia. Entretanto, o MEC foi pouco explorado nessa área e, portanto, existem muitos pontos a serem investidos e estudados. Assim, pode-se sugerir os seguintes temas para trabalhos futuros:
◦ Estudar e estender o programa para caso de aplicação de força tangencial oscilatória e fadiga por fretting;
◦ Extensão do programa para problemas de contato de múltiplos corpos como, por exemplo, cabos condutores;
◦ Extensão para casos tridimensionais;
◦ Extensão para situação de contato dinâmico;
◦ Implementação do MEC isogeométrico e da aproximação cruzada adaptativo (ACA) para a análise de problemas de contato mecânico.
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A
Código computacional da solução analítica Mindlin-Cattaneo
% Soluções analíticas para o problema de contato entre um cilindro e uma % base rígida
% Solução para a tensão normal (p): Solução de Hertz
% Solução para a tensão de cisalhamento (q): Solução de Mindlin-Cattaneo
clear close all
cargav=100; % Valor da carga aplicada na direção vertical
cargah=15; % Valor da carga aplicada na direção horizontal
w=6.5; % Espessura da sapata
R=70; % Raio da sapata
P=2*w*cargav; % Carga total aplicada na direção vertical
Q=2*w*cargah; % Carga total aplicada na direção horizontal
ni=0.33; % Coeficiente de Poisson
E=73.4e3; % Módulo de elasticidade
East=E/(1-ni); % E no estado plano de deformação
a=sqrt(4*R*P/East/pi); % Comprimento da região de contato
xno=-a:a/100:a; % Coordenadas x dos nós
po=2*P/(pi*a); % Valor máximo da tensão normal na reginão de contato
qo=Q/(2*pi*a^2);
mi=cargah/cargav; % Valor mínimo possível para o coeficiente de atrito
for j=1:4 % Loop sob os coeficientes de atrito
c=a*sqrt(1-abs(Q/(mi*P))); % Comprimento da região em adesão
vetmi(j)=mi; % Vetor que guarda os valores dos coeficientes de atrito
for i = 1:size(xno,2) % Loop sobre os nós da região de contato
if(abs(xno(i))<=a) % Verifica se o nó está em contato
p(i)=po*sqrt(1-(xno(i)/a)^2); % tensão normal
q(i,j)=mi*p(i); % tensão de cisalhamento (região em slip)
if(abs(xno(i))<=c) % Verifica se o nó está na região de adesão
qlinha=mi*po*c/a*sqrt(1-(xno(i)/c)^2);
q(i,j)=q(i,j)-qlinha; % tensão de cisalhamento (região % em stick)
end else
p(i)=0; % Valor da tensão normal na região que não está em % contato
% não está em contato
end end
mi=mi+0.05; % Incremento do coeficiente de atrito
end
figure
plot(xno/a,p/po,'bd-',xno/a,q(:,1)/(vetmi(1)*po),'rs-', ...
xno/a,q(:,2)/(vetmi(2)*po),'ko-',xno/a,q(:,3)/(vetmi(3)*po),'g*-', ...
xno/a,q(:,4)/(vetmi(4)*po),'mp-')
leg1=['q para Q/(\mu P) =',num2str(Q/(vetmi(1)*P))]; leg2=['q para Q/(\mu P) =',num2str(Q/(vetmi(2)*P))]; leg3=['q para Q/(\mu P) =',num2str(Q/(vetmi(3)*P))]; leg4=['q para Q/(\mu P) =',num2str(Q/(vetmi(4)*P))]; legend('p/p_o',leg1,leg2,leg3,leg4);
ylabel('Tensões normalizadas') xlabel('{\it x/a}')