ADIFOR: Automatic differentiation in a source translator environment
ISSAC '92 Papers from the international symposium on Symbolic and algebraic computation
Membrane triangles with corner drilling freedoms I: the EFF element
Finite Elements in Analysis and Design
Membrane triangles with corner drilling freedoms II: the ANDES element
Finite Elements in Analysis and Design
Membrane triangles with corner drilling freedoms III: implementation and performance evaluation
Finite Elements in Analysis and Design
Microsystem design
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This paper is concerned with the parameter sensitivity analysis of structures undergoing large displacements. The authors introduce the analytical sensitivity expressions for an element independent co-rotational formulation of a geometrically nonlinear finite element method. An extension of this formulation to treat follower forces is presented. The co-rotational framework uses a pre-existing linear finite element library and does not require the development and implementation of kinematically nonlinear element formulations. This feature along with the element independence makes the co-rotational framework an attractive option for the implementation of geometrically nonlinear analysis and sensitivity analysis capabilities. The sensitivity formulations with respect to shape and material parameters are presented and their numerical treatment is discussed. The importance of a consistent tangent stiffness, including unsymmetric terms, on the accuracy of computed sensitivities is addressed. The framework is applied to shape and topology optimization examples, verifying the methodology and highlighting the importance of accounting for large displacement effects in design optimization problems.