.... Design/methodology/approach An effective total Lagrangian algorithm is designed to extend the element US-ATFH8 to the geometrically nonlinear analysis in which different test and analytical trial functions (ATFs) are employed. Then, the volumetric growth theory of biological tissue is embedded...

... function) to geometrically nonlinear analysis. Design/methodology/approach Based on the assumption that these analytical trial functions can still properly work in each increment step during the nonlinear analysis, the present work concentrates on the construction of incremental nonlinear formulations...

... of the analytical trial functions. R̃ is the prescribed traction along the boundary S_σ: (5) R ̃ = [ T ̃ n − M ̃ n − M ̃ n s ] T u¯ and R¯, respectively, denote the boundary displacement...

... y = − l x * ( l x * 2 + l y * 2 ) 1 2       © Emerald Publishing Limited 2017 Emerald Publishing Limited Licensed re-use rights only Plate bending Finite element methods Analytical trial function Edge effect Hybrid...