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Some Basic Problems Of The Mathematical Theory Of Elasticity

Digital photoelasticity: Recent developments and diverse applications

Proposed auxetic cluster designs for lightweight structural beams with improved load bearing capacity

Metrological considerations in the measurement of contact stress parameters using photoelasticity

Study of auxetic beams under bending: A finite element approach

Experimental studies to exploit photoelastic data of conformal geometries to extract contact parameters are non-existent because closed-form stress field equations were not available until recently. In this paper, the explicit equations recently reported in the literature for a flat punch with rounded edges are generalized so that a single set of equations can be used for a flat punch with rounded edges and Hertzian contacts with arbitrary radii of curvatures. The generality of the governing equations is verified by plotting isochromatics for conformal and non-conformal contact situations. A generic method to evaluate unknown contact parameters from the whole-field isochromatic data for conformal and non-conformal geometries is implemented. The methodology is initially verified using theoretically generated isochromatic data and is then used to experimentally evaluate two contact situations. In view of high-fringe gradient zones, the suitability of various digital photoelastic methods is compared. A novel four-step phase shifting technique is proposed in which isochromatic and isoclinic data can be evaluated using the minimum number of images.

Evaluation of Conformal and Non-Conformal Contact Parameters Using Digital Photoelasticity

A computationally efficient isoparametric tangled finite element method for handling inverted quadrilateral and hexahedral elements

If a ﬁnite element mesh contains concave elements, it is said to tangled. Tangled meshes can occur during mesh generation, mesh optimization, and large deformation simulations, and will lead to erroneous results during ﬁnite element analysis. Recently, the authors introduced the tangled ﬁnite element method (TFEM) to accurately handle tangled 2D concave quadrilateral elements. In this paper, TFEM is extended to 3D hexahedral elements. We demonstrate that TFEM leads to accurate results over tangled hexahedral elements, requiring minimal changes to existing FEM framework.

Towards tangled finite element analysis over partially inverted hexahedral elements

An isoparametric tangled finite element method for handling higher-order elements with negative Jacobian

An important requirement in the standard finite element method (FEM) is that all elements in the underlying mesh must be tangle-free i.e., the Jacobian must be positive throughout each element. To relax this requirement, an isoparametric tangled finite element method (i-TFEM) was recently proposed for linear elasticity problems. It was demonstrated that i-TFEM leads to optimal convergence even for severely tangled meshes. In this paper, i-TFEM is generalized to nonlinear elasticity. Specifically, a variational formulation is proposed that leads to local modification in the tangent stiffness matrix associated with tangled elements, and an additional piece-wise compatibility constraint. i-TFEM reduces to standard FEM for tangle-free meshes. The effectiveness and convergence characteristics of i-TFEM are demonstrated through a series of numerical experiments, involving both compressible and in-compressible problems.

B. C. Prabhune

Papers

Evaluation of Conformal and Non-Conformal Contact Parameters Using Digital Photoelasticity

A computationally efficient isoparametric tangled finite element method for handling inverted quadrilateral and hexahedral elements

Towards tangled finite element analysis over partially inverted hexahedral elements

An isoparametric tangled finite element method for handling higher-order elements with negative Jacobian

Isoparametric Tangled Finite Element Method for Nonlinear Elasticity