Long, Craig SLoveday, Philip WGroenwold, AA2007-06-082007-06-082006-03-12Long, CS, Loveday, PW and Groenwold, AA. 2006. Planar four node Piezoelectric elements with drilling degrees of freedom. International Journal for numerical methods in Engineering, vol 65(11), pp 1802-18300029-5981http://hdl.handle.net/10204/443https://onlinelibrary.wiley.com/doi/abs/10.1002/nme.1524https://doi.org/10.1002/nme.1524Several new planar four node piezoelectric elements with drilling degrees of freedom are presented. The authors begin by deriving two families of variational formulations accounting for piezoelectricity and in-plane rotations. The first family retains the skew-symmetric part of the stress tensor, while in the second; the skew part of stress is eliminated from the functional. The finite elements derived from two of the variational formulations derived in this paper are investigated. The first element is based on an ‘irreducible’ form, while the other is based on a fully mixed functional, with both stress and electric flux density assumed. Our new elements are shown to be accurate and robust in comparison with a number of existing elements, for several benchmark test problems.enPiezoelectricityDrilling degrees of freedomsMixed variational formulationsFinite elementsArticleLong, C. S., Loveday, P. W., & Groenwold, A. (2006). Planar four node Piezoelectric elements with drilling degrees of freedom. http://hdl.handle.net/10204/443Long, Craig S, Philip W Loveday, and AA Groenwold "Planar four node Piezoelectric elements with drilling degrees of freedom." (2006) http://hdl.handle.net/10204/443Long CS, Loveday PW, Groenwold A. Planar four node Piezoelectric elements with drilling degrees of freedom. 2006; http://hdl.handle.net/10204/443.TY - Article AU - Long, Craig S AU - Loveday, Philip W AU - Groenwold, AA AB - Several new planar four node piezoelectric elements with drilling degrees of freedom are presented. The authors begin by deriving two families of variational formulations accounting for piezoelectricity and in-plane rotations. The first family retains the skew-symmetric part of the stress tensor, while in the second; the skew part of stress is eliminated from the functional. The finite elements derived from two of the variational formulations derived in this paper are investigated. The first element is based on an ‘irreducible’ form, while the other is based on a fully mixed functional, with both stress and electric flux density assumed. Our new elements are shown to be accurate and robust in comparison with a number of existing elements, for several benchmark test problems. DA - 2006-03-12 DB - ResearchSpace DP - CSIR KW - Piezoelectricity KW - Drilling degrees of freedoms KW - Mixed variational formulations KW - Finite elements LK - https://researchspace.csir.co.za PY - 2006 SM - 0029-5981 T1 - Planar four node Piezoelectric elements with drilling degrees of freedom TI - Planar four node Piezoelectric elements with drilling degrees of freedom UR - http://hdl.handle.net/10204/443 ER -