This paper proposes and validates a three degrees of freedom element formulation that accounts for torsion and transverse bending of three-dimensional curved elements in explicit numerical analyses methods such as Dynamic Relaxation. Using finite difference modeling, in-plane distortions and moments, the increment of twist (and hence torsion) and out-of-plane bending deformations are determined. Numerical stability and convergence limits of the element are discussed. Two sets of circular arc test cases validate the accuracy of the element against theoretical and six degrees of freedom finiteelement results. This element is widely applicable and found in strained grid shells and spline stressed membranes.
While plants are primarily sessile at the organismal level, they do exhibit a vast array of movements at the organ or sub-organ level. These movements can occur for reasons as diverse as seed dispersal, nutrition, protection or pollination. Their advanced mechanisms generate a myriad of movement typologies, many of which are not fully understood. In recent years, there has been a renewal of interest in understanding the mechanical behavior of plants from an engineering perspective, with an interest in developing novel applications by up-sizing these mechanisms from the micro-to the macro-scale. This literature review identifies the main strategies used by plants to create and amplify movements and anatomize the most recent mechanical understanding of compliant engineering mechanics. The paper ultimately demonstrates that plant movements, rooted in compliance and multi-functionality, can effectively inspire better kinematic/adaptive structures and materials. In plants, the actuators and the deployment structures are fused into a single system. The understanding of those natural movements therefore starts with an exploration of mechanisms at the origins of movements. Plant movements, whether slow or fast, active or passive, reversible or irreversible, are presented and detailed for their mechanical significance. With a focus on displacement amplification, the most recent promising strategies for actuation and adaptive systems are examined with respect to the mechanical principles of shape morphing plant tissues.
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