Exact Three-Dimensional Stability Analysis of Plate Using an Direct Variational Energy Method

In this paper, direct variational calculus was put into practical use to analyses the three dimensional (3D) stability of rectangular thick plate which was simply supported at all the four edges (SSSS) under uniformly distributed compressive load. In the analysis, both trigonometric and polynomial displacement functions were used. This was done by formulating the equation of total potential energy for a thick plate using the 3D constitutive relations, from then on, the equation of compatibility was obtained to determine the relationship between the rotations and deflection. In the same way, governing equation was obtained through minimization of the total potential energy functional with respect to deflection. The solution of the governing equation is the function for deflection. Functions for rotations were obtained from deflection function using the solution of compatibility equations. These functions, deflection and rotations were substituted back into the energy functional, from where, through minimizations with respect to displacement coefficients, formulas for analysis were obtained. In the result, the critical buckling loads from the present study are higher than those of refined plate theories with 7.70%, signifying the coarseness of the refined plate theories. This amount of difference cannot be overlooked. However, it is shown that, all the recorded average percentage differences between trigonometric and polynomial approaches used in this work and those of 3D exact elasticity theory is lower than 1.0%, confirming the exactness of the present theory. Thus, the exact 3D plate theory obtained, provides a good solution for the stability analysis of plate and, can be recommended for analysis of any type of rectangular plates under the same loading and boundary condition. Doi: 10.28991/CEJ-2022-08-01-05 Full Text: PDF

Analytical Study of Bending Characteristics of an Elastic Rectangular Plate using Direct Variational Energy Approach with Trigonometric Function

In this paper, an analytical three-dimensional (3D) bending characteristic of an isotropic rectangular thick plate with all edges simply supported (SSSS) and carrying uniformly distributed transverse load using the energy technique is presented. The three-dimensional constitutive relations which involves six stress components were used in the established, refined shear deformation theory to obtain a total potential energy functional. This theory obviates application of the shear correction factors for the solution to the problem. The governing equation of a thick plate was obtained by minimizing the total potential energy functional with respect to the out of plane displacement. The deflection functions which are in form of trigonometric were obtained as the solution of the governing equation. These deflection functions which are the product of the coefficient of deflection and shape function of the plate were substituted back into the energy functional, thereafter a realistic formula for calculating the deflection and stresses were obtained through minimizations with respect to the rotations and deflection coefficients. The values of the deflections and stresses obtained herein were tabulated and compared with those of previous 3D plate theory, refined plate theories and, classical plate theory (CPT) accordingly. It was observed that the result obtained herein varied more with those of CPT and RPT by 25.39% and 21.09% for all span-to-thickness ratios respectively. Meanwhile, the recorded percentage differences are as close as 7.17% for all span-to-thickness ratios, when compared with three dimensional plate analysis. This showed that exact 3D plate theory is more reliable than the shear deformation theory which are quite coarse for thick plate analysis. Doi: 10.28991/esj-2021-01320 Full Text: PDF

Use of Higher Order Plate Theory in dynamic analysis of SSFS and CSFS thick rectangular plates in orthogonal polynomials

This study applied polynomial expressions as displacement and shear deformation functions in the free-vibration study of thick and moderately thick isotropic rectangular plates. Rectangular plates with two different edge conditions investigated in this work are: one with simple supports at three of its edges and with no support at the other edge denoted with the acronym (SSFS) and a rectangular plate with simple supports at opposite edges while the other opposite edges has a fixed support at one edge and no support at the other edge, this is denoted with the acronym (CSFS). The total potential energy of the plate was derived using the general theory of elasticity. The general governing equation of the plate was derived by minimizing the total potential energy equation of the plate. Edge conditions of the SSFS and CSFS plates were met and substituted into the general governing equation to obtain a linear expression which was solved to generate fundamental natural frequency function for the plates with various span-depth proportion (m/t) and planar dimensions proportion (n/m). The results obtained from this research were found to agree favourably with the results of similar problems in the literature upon comparison.

Determination of the Conditions for Agglomeration of Molybdenite Fines in the Presence of Kerosene Emulsion Through the Extended DVLO Theory

The hydrophobic agglomeration of fine particles of molybdenite in the presence of kerosene emulsion, has been studied in this paper. The results obtained in the investigation as; zeta potential of kerosene emulsion(ζemulsion), zeta potential of the molybdenite sample (ζMoS2), hydrophobicity of molybdenite represented by the contact angle (θMoS2) varying the pH, were used to calculate the total potential energy through the extended DVLO theory. Diagram containing curves total potential energy vs. separation distance of the particles, indicate that increasing the pH, also increases the energy barrier to overcome to achieve agglomeration and viceversa, which translates to a high probability of agglomeration in the pH range 5 to 8, with greater effect as the pH is increased in the acidic region.

Pemanfaatan Kotoran Ternak sebagai Energi Terbarukan Melalui Pembangunan Biodigester Komunal

The potentials of energy from manure waste was calculated in this study aiming to develop biogas utilization in a rural area. The calculation was conducted based on the result from clustering the non-biogas farmer households which cannot afford individual anaerobic digester (AD). Spatial cluster analysis (SCA) and superimposed technique were used to determine the size of the groups and the location of ADs respectively. Value from SCA showed that the village’s settlement pattern is clustered feasible to apply communal AD for rural biogas development. Meanwhile, a superimposed technique using 3 parameters which are land availability, cow ownership, and topography, generates 43 clusters of farmer households that can supply biogas for cooking. The energy production is estimated at 8.96-39.68 m3/day/household, while the energy demand is approximately 0.65-3.48 m3/day/household. The calculation shows that there is remaining biogas that can be distributed to non-biogas farmer households. Using SCA, 75 non-biogas farmer households were identified to be potentially supplied by biogas. The total energy demand for both biogas and non-biogas farmers households is 2,147.34 MJ/day, while the total potential energy generation from all ADs is 24,560.64 MJ/day indicating a low biogas utilization rate which is only 8.7%. The percentage shows that biogas utilization for an energy source in Dusun Dresel can be more developed by enhancing the distribution network or by converting it into electricity to support rural energy security.

An Optimization Method for the Static Balancing of Manipulators Using Springs

This paper discusses a novel optimization method to design statically balanced manipulators. Only springs are used to balance the manipulators composed of revolute (R) joints. Since the total potential energy of the system is constant when statically balanced, the sum of squared differences between the two potential energy when giving different random values of joint variables is set as the objective function. Then the optimization tool of MATLAB is used to obtain the spring attachment points. The results show that for a 1-link manipulator mounted on an R joint, in addition to attaching the spring right above the R joint, the attachment point can have offset. It also indicates that an arbitrary spatial manipulator with n link, whose weight cannot be neglected, can be balanced using n springs. Using this method, the static balancing can be readily achieved, with multiple solutions.

Feasible Numerical Technique for Analysis of Offshore Pipelines and Risers

A simple 2D numerical model for pipeline and riser configuration analyses is presented. The model considers large deformations of the pipe, pipe-seabed contact detection, pipe’s interaction with uneven inelastic seabed, environmental loading such as drag forces applied by the ocean currents, water surface level variations and incorporation of buoyancy modules. The solution technique is based on a consistent minimization of the total potential energy of the deformed pipe discretized as a Riemann sum, which results in a system of nonlinear algebraic finite difference equations that is solved in an incremental/iterative manner. At each increment, the total potential energy is being updated, thus accounting for energy dissipation due to irrecoverable plastic deformation of the seabed and according to hydrodynamic drag forces. The whole pipe is treated as a single continuous segment. To demonstrate the method, examples with several riser configurations and pipe-lay scenarios are presented. It is shown how on-bottom unevenness, including pits and hills, incorporation of buoyancy modules and tidal effects can affect pipeline or riser configurations and their internal forces. Results are compared to those obtained with Abaqus and appear to be in an excellent agreement. The model presents simple and time-efficient way to analyze the pipe-lay or riser configurations with various boundary and loading conditions. The proposed model, contrary to commercial packages, which impose using time-consuming Graphical User Interface (GUI), allows for performing the series of analyses for varying geometric and/or material properties, and processing the results in reasonable time by single click.

Analysis of Orthotropic Thin Rectangular Simply Supported Plate Subjected to both In-Plane Compression and Lateral Loads

This study presents the analysis of thin rectangular orthotropic plate, simply supported at all edges (SSSS) subjected to both in-plane compression and lateral loads. The total potential energy functional was used in the analysis. The general variation of the total potential energy functional was done and the governing equation was obtained. The solution of the direct integration of the governing equation gave the deflection of the plate as a product of the coefficient of deflection and an orthogonal polynomial shape function. The expression for the coefficient of deflection was obtained by the direct variation of the total potential energy functional. This was used to derive the equation for the Lateral load parameter of an orthotropic thin rectangular plate carrying both in-plane compression and lateral loads based on the maximum deflection condition and also based on the elastic stability (yield strength) condition. The peculiar deflection equation for the SSSS plate was obtained using the formulated polynomial shape function. Numerical examples were carried out to determine the lateral load parameters corresponding to various plate thickness and permissible deflection for orthotropic thin SSSS plate carrying both in-plane compression and lateral load. In the same way, the lateral load parameters using the elastic stability condition (yield strength) were obtained for yield strength of 275 MPa, 355 MPa and 410 MPa

A Novel Hybrid Harmony Search Approach for the Analysis of Plane Stress Systems via Total Potential Optimization

By finding the minimum total potential energy of a structural system with a defined degree of freedoms assigned as design variables, it is possible to find the equilibrium condition of the deformed system. This method, called total potential optimization using metaheuristic algorithms (TPO/MA), has been verified on truss and truss-like structures, such as cable systems and tensegric structures. Harmony Search (HS) algorithm methods perfectly found the analysis results of the previous structure types. In this study, TPO/MA is presented for analysis of plates for plane stress members to solve general types of problems. Due to the complex nature of the system, a novel hybrid Harmony Search (HHS) approach was proposed. HHS is the hybridization of local search phases of HS and the global search phase of the Flower Pollination Algorithm (FPA). The results found via HHS were verified with the finite element method (FEM). When compared with classical HS, HHS provides smaller total potential energy values, and needs less iterations than other new generation metaheuristic algorithms.