Chirag Sachdeva

The objective of this work is to obtain closed-form analytical solutions to predict the nonlinear mechanical behavior of bidirectional functionally graded cylindrical beams accurately and faster than the commercially available finite element analysis tools. With the use of variational asymptotic method, the nonlinear three-dimensional elasticity problem is divided into a two-dimensional cross-sectional problem and a one-dimensional problem along the length of the beam. This method makes no ad… Show more

The objective of this work is to obtain closed-form analytical solutions to predict the nonlinear mechanical behavior of bidirectional functionally graded cylindrical beams accurately and faster than the commercially available finite element analysis tools. With the use of variational asymptotic method, the nonlinear three-dimensional elasticity problem is divided into a two-dimensional cross-sectional problem and a one-dimensional problem along the length of the beam. This method makes no ad hoc assumptions but rather takes advantage of small parameters inherent to the beam geometry for solving the problem in an asymptotic sense. The material properties are varied along the axial and the radial directions simultaneously using two distinct power-law parameters. Analytical results for the strains, stresses, curvatures, displacements, and sectional rotations are formulated. The results obtained under different loading conditions and material gradations using the present formulations are compared with the results obtained using three-dimensional analysis in finite element software ABAQUS. Show less

This paper uses Variational Asymptotic Method (VAM) to obtain asymptotically exact analytical solutions for cylinders made up of Functionally Graded Materials (FGM). VAM splits a three-dimensional elasticity problem into a two-dimensional linear cross-sectional problem and a one-dimensional beam problem. It ensures the asymptotic correctness since the method makes no ad hoc assumptions. This is accomplished by taking advantage of certain small parameters inherent to beam-like structures. This… Show more

This paper uses Variational Asymptotic Method (VAM) to obtain asymptotically exact analytical solutions for cylinders made up of Functionally Graded Materials (FGM). VAM splits a three-dimensional elasticity problem into a two-dimensional linear cross-sectional problem and a one-dimensional beam problem. It ensures the asymptotic correctness since the method makes no ad hoc assumptions. This is accomplished by taking advantage of certain small parameters inherent to beam-like structures. This technique has been successfully used for a variety of problems but it has never been implemented on cylinders made up of FGM. Starting with the variable geometry of the cylindrical cross-section made up of radially non-homogeneous material properties controlled by a volume fraction variable, the 3-D problem has been formulated and solved analytically despite the presence of geometrical non-linearities. Closed form analytical solutions are obtained to predict the exact response of functionally graded cylinders. The influence of inner and outer material properties, radius values and the variation trend of material composition on the mechanical behavior is highlighted. Results obtained from the present theory are successfully validated using a commercially available 3-D FEM solver ABAQUS. Analytical solutions obtained can analyze the behavior of any cylinder with FGM quickly and accurately. Show less

The work presented in this paper provides a reliable method to model and analyze smart beams with arbitrary sectional geometries and material properties, including initially curved and twisted beams. It incorporates the modified constitutive equations into the intrinsic equations to formulate a generalized set of solutions applicable for both the actuator and sensor application of piezoelectric smart beams. The radial field problem, sometimes referred to as radially electroded problem, where… Show more

The work presented in this paper provides a reliable method to model and analyze smart beams with arbitrary sectional geometries and material properties, including initially curved and twisted beams. It incorporates the modified constitutive equations into the intrinsic equations to formulate a generalized set of solutions applicable for both the actuator and sensor application of piezoelectric smart beams. The radial field problem, sometimes referred to as radially electroded problem, where the potential is applied on the surfaces along the length (i.e., along the reference line) of the smart beam, is considered in the present study. Three different cases of smart beam geometries are discussed to highlight the capabilities of this method. VABS 4.0, a prerelease version of the variational asymptotic cross-sectional analysis tool for composite beams, is used to obtain the intermediate results containing sectional properties, which are used as inputs into the modified intrinsic equations. The main advantage of this method is its ability to quickly and accurately analyze deformation in smart beams. The values of displacements and rotations obtained along the length can be further used to recover the unknown 3D displacements, stresses and electric potentials using recovery relations. Successful verification of results obtained from the linear equations is presented and is accomplished using a commercially available finite element code ABAQUS. Show less

Composite structures play a vital role in the automobile industry. Use of composites like CFRPs in automobiles poses various problems to engineers. CFRP components are not simple to model in comparison to traditional engineering materials like aluminium, steel etc. One of the main reason is that the composite materials generally do not behave in an isotropic manner but rather behave in an anisotropic or orthotropic manner. These anisotropic and orthotropic mechanical behaviors are more… Show more

Composite structures play a vital role in the automobile industry. Use of composites like CFRPs in automobiles poses various problems to engineers. CFRP components are not simple to model in comparison to traditional engineering materials like aluminium, steel etc. One of the main reason is that the composite materials generally do not behave in an isotropic manner but rather behave in an anisotropic or orthotropic manner. These anisotropic and orthotropic mechanical behaviors are more difficult to predict as compared to isotropic behaviors. This problem is solved using finite element analysis (FEA) packages to model complex composite material and predict their behavior. The paper discusses about the propagation of stresses within the composite laminates using FEA in Abaqus for different lamina stacking directions. The results obtained are verified using Theoretical Analysis in MATLAB. Such analysis can be used to analyze high performance composite components containing multiple plies quickly and more effectively. Show less