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Tdgl equation piezo electric12/10/2023 ![]() The feasibility of the proposed models is confirmed by finite element analysis and by experiments under various elastic loads. Some original findings differing from the well-known constitutive performance of piezo-stacks are also given. Also significantly, a new model of output displacement for compliant mechanism interacting with piezo-stacks and elastic loads is deduced based on the generalized constitutive equations. In keeping with the familiar piezoelectric constitutive equations, the generalized constitutive equations of compliant mechanism represent the input-output displacement and force relations in the form of a generalized Hooke’s law and as analytical functions of physical parameters. This paper formulates analytical models to describe the static displacement and force interactions between generic serial-parallel compliant mechanisms and their loads by employing the matrix method. Generalized constitutive equations for piezo-actuated compliant mechanismĬao, Junyi Ling, Mingxiang Inman, Daniel J. On the contrary, those empirical equations have low prediction capabilities due to constant parameters and poor applicability because of the limit of special strain path or parameter conditions based on strict phenomenology. Analysis results indicated that the constitutive equation with varying parameters could characterize superplastic flow behavior in practical superplastic forming with high prediction accuracy and without any restriction of strain path or deformation condition, showing good industrial or scientific interest. The superplastic tension test data of Zn-5%Al alloy at 340 Â☌ under strain rates, velocities, and loads were employed for building a new constitutive equation and examining its validity. Subsequently, a new, general constitutive equation with varying parameters was theoretically deduced based on the general mechanical equation of state. From the view of phenomenology, firstly, some traditional empirical constitutive relations were standardized by restricting some strain paths and parameter conditions, and the coefficients in these relations were strictly given new mechanical definitions. In this study, constitutive equations for superplastic materials with an extra large elongation were investigated through mechanical analysis. Guan, Zhiping Ren, Mingwen Jia, Hongjie Zhao, Po Ma, Pinkui The example of construction of hereditary constitutive equations of cross-ply carbon fiber-reinforced plastic is presented.Ĭonstitutive Equation with Varying Parameters for Superplastic Flow Behavior Effective matrix algorithm and relationships of operator algebra are used to derive visco-elastic stiffness and compliance of the laminate. ![]() ![]() The constitutive equations of the laminate are constructed on the basis of classical laminate theory and algebra of resolvent operators. The method is developed from the assumption that in the directions of axes of orthotropy the layer follows elastic behavior, and obeys hereditary constitutive equations under shear. Tairova, Lyudmila P.Ī method for the construction of hereditary constitutive equation is proposed for the laminate on the basis of hereditary constitutive equations of a layer. A Method for the Construction of Hereditary Constitutive Equations of Laminates Bases on a Hereditary Constitutive Equation for a Layerĭumansky, Alexander M.
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