Correction to: Journal of Elasticity (2018) 131: 239–276 https://doi.org/10.1007/s10659-017-9654-1

  1. 1.

    In the right hand sides of Eqs. (39), (55)–(58), (59)–(62), (74)–(76), and (78)–(80), replace the partial derivative operator with \(\tilde{\partial }\).

  2. 2.

    Consequent to Item 1, Eqs. (68)–(70) should be replaced by

    $$\begin{aligned} K_{1212}+[b_{11}b_{22}-b^{2}_{12}] =&4\partial _{[1}(\sqrt{a}\, a_{2] \sigma } J^{\sigma }) -2C_{[1|\mu 2|}\, C_{2]1}{}^{\mu }-a(J^{3})^{2} , \\ -\partial _{2} b_{1 1}+\partial _{1} b_{1 2} =& \partial _{1}(\sqrt{a}J^{3}) + 2a J^{2} J^{3} + 2\sqrt{a} J^{\sigma }(b^{2}_{1} a_{\sigma 2} - b^{2}_{2} a_{\sigma 1}), \\ -\partial _{2} b_{2 1}+\partial _{1} b_{2 2} =& \partial _{2}(\sqrt{a}J^{3}) - 2a J^{1} J^{3} ++ 2\sqrt{a} J^{\sigma }(b^{1}_{2} a_{\sigma 1} - b^{1}_{1} a_{\sigma 2}). \end{aligned}$$

    Henceforth, Eqs. (82)–(83) and (84)1 should be

    $$\begin{aligned} \Lambda ^{p}_{11}\Lambda ^{p}_{22} - (\Lambda ^{p}_{(12)})^{2} =& 2(J^{2}_{,1}-J^{1}_{,2} ) -(J^{3})^{2}, \\ \Lambda ^{p}_{1 1,2}- \Lambda ^{p}_{(1 2),1} =& J^{3}_{,1} + 2J^{2} J^{3} + 2 J^{1} \Lambda ^{p}_{22} - 2 J^{2} \Lambda ^{p}_{(12)}, \\ \Lambda ^{p}_{(12 ),2}- \Lambda ^{p}_{2 2,1} =& J^{3}_{,2} - 2 J^{1} J^{3} + 2 J^{2} \Lambda ^{p}_{11} - 2 J^{1} \Lambda ^{p}_{(12)}. \end{aligned}$$

    These three relations have earlier appeared as Eq. 35.82 in Derezin, Shell-like Structures, Vol. 15, pp. 531–547. Springer, 2011.

  3. 3.

    In Eqs. (74) and (91), the term \(2\sqrt{A}\, A_{\sigma[1} \bar{\partial }_{2]}J^{\sigma}\) should be replaced by \(-4\sqrt{A}\, A_{\sigma[1} \tilde{\partial}_{2]}J^{\sigma}\).