• Steel and Composite Structures
• /
• v.48 no.5
• /
• pp.583-597
• /
• 2023

This paper introduces a novel approach to multi-material topology optimization (MTO) targeting in-plane bi-directional functionally graded (IBFG) non-uniform thickness Reissner-Mindlin plates, employing an alternative active phase approach. The mathematical formulation integrates a first shear deformation theory (FSDT) to address compliance minimization as the objective function. Through an alternating active-phase algorithm in conjunction with the block Gauss-Seidel method, the study transforms a multi-phase topology optimization challenge with multi-volume fraction constraints into multiple binary phase sub-problems, each with a single volume fraction constraint. The investigation focuses on IBFG materials that incorporate adequate local bulk and shear moduli to enhance the precision of material interactions. Furthermore, the well-established mixed interpolation of tensorial components 4-node elements (MITC4) is harnessed to tackle shear-locking issues inherent in thin plate models. The study meticulously presents detailed mathematical formulations for IBFG plates in the MTO framework, underscored by numerous numerical examples demonstrating the method's efficiency and reliability.

• Architectural research
• /
• v.18 no.2
• /
• pp.65-74
• /
• 2016

Free vibration analysis of plates and shells is carried out by using isogeometric approach. For this purpose, an isogeometric shell element based on Reissner-Mindlin (RM) shell theory is developed. Non-uniform rational B-spline surface (NURBS) definition is introduced to represent the geometry of shell and it is also used to derive all terms required in the isogeometric element formulation. New anchor positions are proposed to calculate the shell normal vector. Gauss integration rule is used for the formation of stiffness and mass matrices. The proposed shell element is then used to examine vibrational behaviours of plate and shell structures. From numerical results, it is found to be that reliable natural frequencies and associated mode shapes can be predicted by the present isogeometric RM shell element.

• Proceedings of the Computational Structural Engineering Institute Conference
• /
• 2007.04a
• /
• pp.663-668
• /
• 2007

An enhanced first shear deformation theory for composite plate is developed. The detailed process is as follows. Firstly, the theory is formulated by modifying higher order zigzag theory. That is, the higher order theory is separated into the warping function representing the higher order terms and lower order terms. Secondly, the relationships between higher order zig-zag field and averaged first shear deformation field based on the Reissner-Mindlin's plate theory are derived. Lastly, the effective shear modulus is calculated by minimizing error between higher order energy and first order energy. Then the governing equation of FSDT is solved by substituting shear modulus into effective shear modulus. The recovery processing with the nodal unknown obtained from governing equation is performed. The accuracy of the present proposed theory is demonstrated through numerical examples. The proposed method will serve as a powerful tool in the prediction of laminated composite plate.

• Computational Structural Engineering
• /
• v.3 no.3
• /
• pp.101-111
• /
• 1990

The elastic analysis of floor slabs using the p-version of finite element method encounters stress singularities at certain types of reentrant corners, openings and cut-outs. Results obtained using the computer code based on C.deg. - hierarchic plate element formulated by Reissner-Mindlin theory are compared with theoretical predictions and with computational results reported in the literature. The convergence rate of h-, p- and hp-version can be estimated on the basis of the energy norm in global sense. If accuracy in terms of the number of degree-of-freedom is used as a criterion, the solutions presented here are the most efficient that have been published up to date. Examples are the rhombic plate with the obtuse angle of 150.deg. and the square plate with cut-outs.

• Journal of Korean Association for Spatial Structures
• /
• v.7 no.5
• /
• pp.67-74
• /
• 2007

The unsymmetrically layered artificial material model is consistently introduced to find the optimum topologies of the plate structures. Reissner-Mindlin (RM) plate theory is adopted to formulate the present 9-node plate element considering the first-order shear deformation of the plates. In the topology optimization process, the strain energy to be minimized is employed as the objective function and the initial volume of structures is adopted as the constraint function. In addition, the resizing algorithm based on the optimality criteria is used to update the hole size introduced in the proposed artificial material model. Several numerical examples are rallied out to investigate the performance of the proposed technique. From numerical results, the proposed topology optimization techniques are found to be very effective to produce the optimum topology of plate structures. In particular, the proposed unsymmetric stiffening layer model make it possible to produce more realistic stiffener design of the plate structures.

• Structural Engineering and Mechanics
• /
• v.40 no.4
• /
• pp.501-515
• /
• 2011

Sandwich elements have high flexural rigidity and high strength per density. They also have excellent anti-vibration and anti-noise characteristics. Therefore, they are used for structures of airplanes and high speed ships that must be light, as well as strong. In this paper, the Reissner-Mindlin's plate theory is studied from a Hamilton's principle point of view. This theory is modified to include the influence of shear deformation and rotary inertia, and the equation of motion is derived using energy relationships. The theory is applied to a rectangular sandwich model which has isotropic, asymmetrical faces and an isotropic core. Investigations are conducted for five different plate thicknesses. These plates are identical to the sandwich plates currently used in various structural elements of surface effect ships (SES). The boundary conditions are set to simple supports and fixed supports. The elastic and shear moduli are obtained from the four-point bending tests on the sandwich beams.

• Structural Engineering and Mechanics
• /
• v.40 no.1
• /
• pp.121-148
• /
• 2011

Closed form solutions for equilibrium and flexibility matrices of the Mindlin-Reissner theory based eight-node rectangular plate bending element (MRP8) using Integrated Force Method (IFM) are presented in this paper. Though these closed form solutions of equilibrium and flexibility matrices are applicable to plate bending problems with square/rectangular boundaries, they reduce the computational time significantly and give more exact solutions. Presented closed form solutions are validated by solving large number of standard square/rectangular plate bending benchmark problems for deflections and moments and the results are compared with those of similar displacement-based eight-node quadrilateral plate bending elements available in the literature. The results are also compared with the exact solutions.

• Journal of Korean Association for Spatial Structures
• /
• v.14 no.2
• /
• pp.59-68
• /
• 2014

A study on the vibration and buckling analyses of laminated composite plates is described in this paper. In order to carry out the analyses of laminated composite plates, a NURBS-based isogeometric general plate element based on Reissner-Mindlin (RM) theory is developed. The non-uniform rational B-spline (NURBS) is used to represent the geometry of plate and the unknown displacement field and therefore, all terms required in this element formulation are consistently derived by using NURBS basis function. Numerical examples are conducted to investigate the accuracy and reliability of the present plate element. From numerical results, the present plate element can produce the isogeometric solutions with sufficient accuracy. Finally, the present isogeometric solutions are provided as future reference solutions.

• Advances in materials Research
• /
• v.12 no.2
• /
• pp.83-100
• /
• 2023

In this paper, sandwich plate, constructed with orthotropic and isotropic composite materials, is analyzed to obtain the static and harmonic behavior. The analysis is done by using ANSYS APDL FEM tool. A solid-shell 190 and an 8-node solid 185 elements are employed for face and core material respectively to analyze the plate. Results was attained by using Reissner-Mindlin theory. Effect of increasing thickness ratio of face sheet to depth of the plate is presented on static, vibration and harmonic response on the sheet and the results are discussed briefly. Published work in open domain was used to validate the results and observed excellent agreement. It can be stated that proposed model presents results with remarkable accuracy. Results are obtained to reduce the weight of the plate and minimizing the vibration amplitudes.

• Structural Engineering and Mechanics
• /
• v.4 no.2
• /
• pp.149-162
• /
• 1996

A postbuckling analysis is presented for a simply supported, moderately thick rectangular plate subjected to combined axial compression and uniform temperature loading and resting on a two-parameter elastic foundation. The two cases of thermal postbuckling of initially compressed plates and of compressive postbuckling of initially heated plates are considered. The initial geometrical imperfection of the plate is taken into account. The formulations are based on the Reissner-Mindlin plate theory considering the first order shear deformation effect, and including the plate-foundation interaction and thermal effect. The analysis uses a deflection-type perturbation technique to determine the buckling loads and postbuckling equilibrium paths. Numerical examples cover the performances of perfect and imperfect, moderately thick plates resting on Winkler or Pasternak-type elastic foundations. Typical results are presented in dimensionless graphical form.