In this paper, a triangular planar element is developed for a geometrically nonlinear structural analysis, which includes the drilling degrees of freedom using a corotational framework. Based on the assumptions of a small degree of strain and large displacement, the corotational framework allows an accurate geometrically nonlinear structural analysis. The presently improved corotational framework accommodates in-plane rotational behavior (that is, the drilling degrees of freedom) by using the corotational framework corresponding to a solidlike planar element. It focuses on triangular planar elements that will be useful for three-dimensional analysis using a reduced number of degrees while targeting a structure with a complex geometry, such as a flapping wing. Regarding the present analysis, validation by solving both static and time-transient problems is conducted. The fluid–structure interaction framework is then developed by using the present structural analysis. During this validation procedure, the present results are compared with those obtained with three-dimensional solid elements provided by the commercial software ANSYS. Finally, a relevant fluid–structure interaction analysis for the flapping wing is conducted and an examination of the usefulness of the present planar element is done through comparisons between experimental results and those obtained in earlier studies.