TSDT theory for free vibration of functionally graded plates with various material properties

In this work, an implicit algorithm is used for analyzing the free dynamic behavior of Functionally Graded Material (FGM) plates. The Third order Shear Deformation Theory (TSDT) is used to develop the proposed model. In this contribution, the formulation is written without any homogenization technique as the rule of mixture. The Hamilton principle is used to establish the resulting equations of motion. For spatial discretization based on Finite Element Method (FEM), a quadratic element with four and eight nodes is adopted using seven degrees of freedom per node. An implicit algorithm is used for solving the obtained problem. To study the accuracy and the performance of the proposed approach, we present comparisons with literature and laminate composite modeling results for vibration natural frequencies. Otherwise, we examine the influence of the exponent of the volume fraction which reacts the plates "P-FGM" and "S-FGM". In addition, we study the influence of the thickness on "E-FGM" plates.

Composite modeling of leaf shape across shoots discriminates Vitis species better than individual leaves

ABSTRACTPremise of studyLeaf morphology is dynamic, continuously deforming during leaf expansion and among leaves within a shoot. We measured leaf morphology from over 200 vines over four years, and modeled changes in leaf shape along the shoot to determine if a composite “shape of shapes” can better capture variation and predict species identity compared to individual leaves.MethodsUsing homologous universal landmarks found in grapevine leaves, we modeled various morphological features as a polynomial function of leaf node. The resulting functions are used to reconstruct modeled leaf shapes across shoots, generating composite leaves that comprehensively capture the spectrum of possible leaf morphologies.ResultsWe found that composite leaves are better predictors of species identity than individual leaves from the same plant. We were able to use composite leaves to predict species identity of previously unassigned vines, which were verified with genotyping.DiscussionObservations of individual leaf shape fail to capture the true diversity between species. Composite leaf shape—an assemblage of modeled leaf snapshots across the shoot—is a better representation of the dynamic and essential shapes of leaves, as well as serving as a better predictor of species identity than individual leaves.