Showing papers on "Displacement field published in 2022"

Mechanical behavior and free vibration analysis of FG doubly curved shells on elastic foundation via a new modified displacements field model of 2D and quasi-3D HSDTs

Abstract: Analysis of the effect of Pasternak’s elastic foundation parameters on the bending and free vibration of functionally graded double curved shells subjected to uniform and sinusoidal loads is the purpose of this paper in which the novelty is to develop a new formulated 2D and quasi-3D HSDT shell theories with considering the effect of transverse shear and shell thickness stretching. Numerical results are reported for different geometries including plates, cylindrical and spherical shells using a five-variable displacement field in terms of undetermined integrals by employing a trigonometric-exponential hybrid function. The impact of geometrical parameters, volume fraction and foundation stiffness on the static and vibratory behaviors​ is extensively discussed. Convergence studies and error analysis are carried out to validate the present approach. The proposed theory proves to be simple and useful in the analysis of double-curved FGM shells.

Nonlocal vibration of functionally graded nanoplates using a layerwise theory

Abstract: This work studies the size-dependent free vibration response of functionally graded (FG) nanoplates using a layerwise theory. The proposed model supposes not only a higher-order displacement field for the core but also the first-order displacement field for the two face sheets, thereby maintaining an interlaminar displacement continuity among layers. Unlike the conventional layerwise models, the number of variables is kept fixed and does not increase for an increased number of layers. This is a very important feature compared to conventional layerwise models and facilitates significantly the engineering analyses. The material properties of the FG nanoplate are graded continuously through the thickness direction in accordance with a power-law function. The Eringen’s nonlocal elasticity theory is here adopted to relax the continuum axiom required in classical continuum mechanics and hence hopeful to capture the small size effects of naturally discrete nanoplates. The equations of motion of the problem are obtained via a classical Hamilton’s principle. The present layerwise model is implemented with a computationally efficient C0- continuous isoparametric serendipity elements and applied to solve a large-scale discrete numerical problem. The robustness and reliability of the developed finite element model are demonstrated by a comparative evaluation of results against predictions from literature. The comparative studies show that the proposed finite element model is: (a) free of shear locking, (b) accurate with a fast rate convergence for both thin and thick FG nanoplates, and (c) excellent in terms of numerical stability. Moreover, a detailed parametric analysis checks for the sensitivity of the vibration response of FG nanoplates to the aspect ratio, length-to-thickness ratio, nonlocal parameter, boundary conditions, power-law index, and modes shapes. Referential results are also reported, for the first time, for natural frequencies of FGM nanoplates which will serve as benchmarks for further computational investigations.

A Unified Full-Field Deformation Measurement Method for Beam-Like Structure

Abstract: Full-field displacement reconstruction, which uses a few strain sensors for obtaining real-time surface strain as the input data of the monitoring system, is a crucial technology to actuate and control smart structures. In the previous reconstruction algorithm, the displacement vectors consistent with some particular kinematic assumptions of the deformation theory should be determined in advance. However, obtaining the displacement vectors of complex structures accurately and quickly is difficult in engineering. Therefore, the attentions are mainly on seeking a unified method to avoid the reconstruction errors caused by structural misidentification. For this purpose, some particular generalized quantities are adopted to replace the traditional displacement functions, and the unified displacement field of beam-like structures is proposed based on the homogenized theory. Meanwhile, the reconstruction function is established based on the classic inverse finite-element method (iFEM). Next, the transformation relationships are determined between the generalized numerical strains and the measured strains using a tailored strain measurement scheme. Finally, several beam-like structures with different slenderness ratios are used as the test examples to verify the reliability and effectiveness of the presented full-field displacement monitoring method. The simulation and experimental results demonstrate the superior precision and stable reliability of the presented measurement method for performing shape sensing of beam-like structures.

Phase‐field modeling of brittle fracture along the thickness direction of plates and shells

Abstract: The prediction of fracture in thin‐walled structures is decisive for a wide range of applications. Modeling methods such as the phase‐field method usually consider cracks to be constant over the thickness which, especially in load cases involving bending, is an imperfect approximation. In this contribution, fracture phenomena along the thickness direction of structural elements (plates or shells) are addressed with a phase‐field modeling approach. For this purpose, a new, so called “mixed‐dimensional” model is introduced, which combines structural elements representing the displacement field in the two‐dimensional shell midsurface with continuum elements describing a crack phase‐field in the three‐dimensional solid space. The proposed model uses two separate finite element discretizations, where the transfer of variables between the coupled two‐ and three‐dimensional fields is performed at the integration points which in turn need to have corresponding geometric locations. The governing equations of the proposed mixed‐dimensional model are deduced in a consistent manner from a total energy functional with them also being compared to existing standard models. The resulting model has the advantage of a reduced computational effort due to the structural elements while still being able to accurately model arbitrary through‐thickness crack evolutions as well as partly along the thickness broken shells due to the continuum elements. Amongst others, the higher accuracy as well as the numerical efficiency of the proposed model are tested and validated by comparing simulation results of the new model to those obtained by standard models using numerous representative examples.

Analysis of metallic and functionally graded beams using isogeometric approach and Carrera Unified Formulation

Abstract: Abstract This paper investigates the bending and vibration characteristics of metallic and functionally graded (FG) beam structures. The weak form of governing equations and boundary conditions are derived using Carrera unified formulation (CUF). The isogeometric analysis (IGA) is employed to solve the static and free vibration problems. NURBS basis functions approximate the displacement field unknowns and material gradations in cross-section. In contrast, the axial displacements are evaluated by either NURBS or Lagrange basis functions. In this framework, the equations are extracted in the form of a fundamental nucleus, which allows the study of different beam theories in a constant formulation. Several numerical examples are presented and compared with results available in the literature to address the accuracy and effectiveness of the current approach. It is found that the present results are validated for different aspect ratios, boundary conditions, and material distribution with more accuracy and low computational cost.

Nonlinear thermomechanical analysis of CNTRC cylindrical shells using HSDT enriched by zig-zag and polyconvex strain cover functions

Abstract: A new higher-order shear deformation zig-zag theory enriched by polyconvex strain cover functions is proposed for predicting the nonlinear stability characteristics of thermo mechanically loaded carbon nanotube-reinforced composite (CNTRC) laminated cylindrical shells surrounded by elastic foundations. The thermomechanical properties of composite laminated shells are considered to be temperature-dependent and are evaluated using the extended rule of mixture method. The von Kármán strain field is adopted to describe the structural nonlinearity of the composite laminated shells. The proposed higher-order shear deformation zig-zag theory employs polyconvex strain variables to represent the displacement field of the composite shell in a unified form. The nonlinear behavior is modeled using the stability equations in axisymmetric and non-axisymmetric buckling. The validity of the present analytical model is confirmed by comparing the computed results with those solutions available in the literature. The nonlinear behavior of CNTRC laminated shells with different geometrical dimensions, temperature gradients, and distribution patterns is investigated. Moreover, the stress analysis of CNTRC cylindrical shells under thermal environments is performed.

A simple refined plate theory for the analysis of bending, buckling and free vibration of functionally graded porous plates reinforced by graphene platelets

Abstract: This paper presents a simple refined plate theory (S-RPT) which contains only three unknown variables in the displacement field for bending and buckling analysis and only one unknown variable in the displacement field for free vibration analysis. Unlike other simplified plate theories, S-RPT in its simplification (1) takes into account the Poisson’s ratio variation along the thickness direction (2) takes into account the full coupling of in-plane and transverse displacements. These features make S-RPT applicable to the analysis of bending, buckling, and free vibration of functionally graded porous plates reinforced with graphene platelets (FGP–GPLs). Some simplified plate theories already available in the literature can be regarded as special cases of S-RPT. The S-RPT is first used in isotropic and metal–ceramic functionally graded plates to verify its accuracy. Then, the effect of pore distribution, GPLs distribution, porosity coefficient, aspect ratio, thickness ratio, and GPLs weight fraction on the bending, buckling, and free vibration behaviors are investigated based on S-RPT.

Thermo-mechanical coupling analysis of laminated composite plates using wavelet finite element method

Abstract: This paper proposes a novel high performance wavelet finite element formulation for thermo-mechanical coupling analysis of laminated composite plates. The Reddy’s higher-order shear deformation theory (HSDT) adopted for theoretical formulation represents parabolic variation of transverse shear stresses through thickness to take into account the effects of transverse shears and traction-free boundary conditions for laminated composite plates. The governing equations involving displacement field and temperature gradient field in term of the thickness variable are derived by implementing the principle of virtual work. Then the B-spline wavelet on the interval (BSWI) wavelet-based element is constructed by means of scaling functions as approximating functions instead of polynomial interpolations used in traditional finite element method (FEM). The convergence, accuracy and efficiency of proposed BSWI wavelet-based method are verified for mechanical and thermal analysis of laminated composite plates with fewer degrees of freedom. Then numerical examples concerning various length-to-thickness ratios, aspect ratios and stacking sequences are investigated for thermo-mechanical coupling analysis of symmetric and anti-symmetric laminated composite plates. These comparison examples demonstrate the accuracy and reliability of the proposed BSWI wavelet-based method comparing with the three-dimensional elasticity solutions and referential numerical solutions available in literatures.