A Non Linear Shell Theory Compared With the Classical Three Dimensional Theory O
A Non Linear Shell Theory Compared With the Classical Three Dimensional Theory O
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A, .^, Q = Q j^j4-H^(Q), C(Q^j|'^'- Q^j.^j) = (1 + Gq)H^(Q) = H^(Q) CQ^jH' = (l+S)Qij^j + H^(Q) = Q^, j + Ji(Q) = V^+ S' + J^(Q) Considering V. As a function of displacements, it is seen that V is an nth degree polynomial in 0^ and V^ is an (n+l)st ex p P degree polynomial. Hence 37 — e — ^a= Z^a(k)^lc(Tf) = Z. '«"j, J-2aJ, j'(K)Pk(Tr) 'from the k=0 k=0 ieflnitions of S . . And V. ) 1 J 1 ^[CQ°'^. |J + J^(Q)+ S'](j^)P^(^) from (6.^) k=0 — i 2FnPk+l(^)[(Q°^jl'+F")C](^) from (6. 2) k=n-l 2^[-F%Ho...(F) + J^(Q)+s'](^jP^(-jf) k=0 + i 2FfTPk+l(TfHVa-^S +J^(Q)+F°'+Ho(F)](j^) k=n-l from (6. 4) For k = n- 1, n ^a(k) = f%, p+^'(u", 33+U^, 3a^](k)^^^°'" *^^ definitions of M^ ) (^ap, p + ^U^, 3a)(k) since U ^^^ is an (n-2)nd degree polynomial in 6^ if n > 2 and is zero if n = 1.
38 Hence n ^a= I [-''" + Jo
To quickly assess the difficulty of the text, read a short excerpt:
A, .^, Q = Q j^j4-H^(Q), C(Q^j|'^'- Q^j.^j) = (1 + Gq)H^(Q) = H^(Q) CQ^jH' = (l+S)Qij^j + H^(Q) = Q^, j + Ji(Q) = V^+ S' + J^(Q) Considering V. As a function of displacements, it is seen that V is an nth degree polynomial in 0^ and V^ is an (n+l)st ex p P degree polynomial. Hence 37 — e — ^a= Z^a(k)^lc(Tf) = Z. '«"j, J-2aJ, j'(K)Pk(Tr) 'from the k=0 k=0 ieflnitions of S . . And V. ) 1 J 1 ^[CQ°'^. |J + J^(Q)+ S'](j^)P^(^) from (6.^) k=0 — i 2FnPk+l(^)[(Q°^jl'+F")C](^) from (6. 2) k=n-l 2^[-F%Ho...(F) + J^(Q)+s'](^jP^(-jf) k=0 + i 2FfTPk+l(TfHVa-^S +J^(Q)+F°'+Ho(F)](j^) k=n-l from (6. 4) For k = n- 1, n ^a(k) = f%, p+^'(u", 33+U^, 3a^](k)^^^°'" *^^ definitions of M^ ) (^ap, p + ^U^, 3a)(k) since U ^^^ is an (n-2)nd degree polynomial in 6^ if n > 2 and is zero if n = 1.
38 Hence n ^a= I [-''" + Jo
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