88 Real
stress(
const Real w,
const Real t,
const int deriv = 0,
const int comp1 = 0,
const int comp2 = 0)
const {
89 const Real scale(600), X(500), Y(1000);
92 val = scale*(Y/(w*t*t) + X/(w*w*t));
94 else if (deriv == 1) {
97 val = scale*(-Y/(w*w*t*t) - two*X/(w*w*w*t));
99 else if (comp1 == 1) {
101 val = scale*(-two*Y/(w*t*t*t) - X/(w*w*t*t));
104 else if (deriv == 2) {
105 if (comp1 == 0 && comp2 == 0) {
106 const Real two(2), six(6);
107 val = scale*(two*Y/(w*w*w*t*t) + six*X/(w*w*w*w*t));
109 else if (comp1 == 1 && comp2 == 1) {
110 const Real two(2), six(6);
111 val = scale*(six*Y/(w*t*t*t*t) + two*X/(w*w*t*t*t));
113 else if (comp1 == 0 && comp2 == 1) {
115 val = scale*two*(Y/(w*w*t*t*t) + X/(w*w*w*t*t));
117 else if (comp1 == 1 && comp2 == 0) {
119 val = scale*two*(Y/(w*w*t*t*t) + X/(w*w*w*t*t));
125 Real
displacement(
const Real w,
const Real t,
const int deriv = 0,
const int comp1 = 0,
const int comp2 = 0)
const {
126 const Real four(4), L(100), E(2.9e7), X(500), Y(1000);
127 const Real C = four*std::pow(L,3)/E;
128 Real arg1 = std::pow(Y/(t*t),2), arg2 = std::pow(X/(w*w),2);
129 Real mag = std::sqrt(arg1 + arg2);
134 else if (deriv == 1) {
137 val = -C * (three * std::pow(X*t*t,2) + std::pow(Y*w*w,2))
138 / (std::pow(w,6)*std::pow(t,5)*mag);
140 else if (comp1 == 1) {
142 val = -C * (std::pow(X*t*t,2) + three*std::pow(Y*w*w,2))
143 / (std::pow(w,5)*std::pow(t,6)*mag);
146 else if (deriv == 2) {
147 if (comp1 == 0 && comp2 == 0) {
148 const Real two(2), six(6), nine(9);
149 val = C * two * mag * (std::pow(Y*w*w,4) + nine*std::pow(Y*X*w*w*t*t,2) + six*std::pow(X*t*t,4))
150 / (std::pow(w,3)*t*std::pow(std::pow(Y*w*w,2)+std::pow(X*t*t,2),2));
152 else if (comp1 == 1 && comp2 == 1) {
153 const Real two(2), six(6), nine(9);
154 val = C * two * mag * (six*std::pow(Y*w*w,4) + nine*std::pow(Y*X*w*w*t*t,2) + std::pow(X*t*t,4))
155 / (std::pow(t,3)*w*std::pow(std::pow(Y*w*w,2)+std::pow(X*t*t,2),2));
157 else if (comp1 == 0 && comp2 == 1) {
158 const Real two(2), three(3);
159 val = C * (three*std::pow(X*t*t,4) + two*std::pow(X*Y*t*t*w*w,2) + three*std::pow(Y*w*w,4))
160 / (std::pow(t*w,6)*mag*(std::pow(X*t*t,2) + std::pow(Y*w*w,2)));
162 else if (comp1 == 1 && comp2 == 0) {
163 const Real two(2), three(3);
164 val = C * (three*std::pow(X*t*t,4) + two*std::pow(X*Y*t*t*w*w,2) + three*std::pow(Y*w*w,4))
165 / (std::pow(t*w,6)*mag*(std::pow(X*t*t,2) + std::pow(Y*w*w,2)));