The absolute nodal coordinate formulation was originally developed for the analysisof structures undergoing large rotations and deformations. This dissertationproposes several enhancements to the absolute nodal coordinate formulationbased finite beam and plate elements. The main scientific contribution of thisthesis relies on the development of elements based on the absolute nodal coordinateformulation that do not suffer from commonly known numerical lockingphenomena. These elements can be used in the future in a number of practicalapplications, for example, analysis of biomechanical soft tissues. This studypresents several higher-order Euler–Bernoulli beam elements, a simple methodto alleviate Poisson’s and transverse shear locking in gradient deficient plateelements, and a nearly locking free gradient deficient plate element.The absolute nodal coordinate formulation based gradient deficient plate elementsdeveloped in this dissertation describe most of the common numerical lockingphenomena encountered in the formulation of a continuum mechanics baseddescription of elastic energy. Thus, with these fairly straightforwardly formulatedelements that are comprised only of the position and transverse direction gradientdegrees of freedom, the pathologies and remedies for the numerical lockingphenomena are presented in a clear and understandable manner. The analysis ofthe Euler–Bernoulli beam elements developed in this study show that the choiceof higher gradient degrees of freedom as nodal degrees of freedom leads to asmoother strain field. This improves the rate of convergence.
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