#### Applied Mechanics

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EISSN : 0018-0018
Total articles ≅ 58
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Published: 15 October 2021
by MDPI
Applied Mechanics, Volume 2, pp 841-848; https://doi.org/10.3390/applmech2040048

Abstract:
In a flexoelectric sensing element using bending mode, estimation of the flexoelectric coefficient was investigated using 3-D stress/strain analysis and experiments. The proposed method uses the results (deformation and strain) from the finite element analysis (FEA). The estimated flexoelectric coefficients were compared with those obtained via the conventional method (Euler’s beam theory) under the assumption of the quasi 1-D stress field. The results show that the RMS value and standard deviation of the estimated flexoelectric coefficient for the 3-D stress field case of the sensing element are 31.51 µC/m and 0.24%, respectively. In addition, we found that the flexoelectric coefficient obtained from the results of the 3-D stress analysis is 1.8% smaller than that of the quasi-1-D stress analysis. Therefore, in order to obtain a more reliable flexoelectric coefficient in the sensing element, the results of the 3-D numerical stress analysis should be used for accurate estimation of the flexoelectric coefficient.
Published: 14 October 2021
by MDPI
Applied Mechanics, Volume 2, pp 820-840; https://doi.org/10.3390/applmech2040047

Abstract:
Existing reinforced concrete (RC) buildings in Europe have generally been designed without proper consideration of seismic actions and capacity design principles, and thus they tend to be vulnerable to earthquakes. Moreover, since a significant proportion of the aforementioned buildings were developed during the 1950s and 1960s, they are currently close to the end of their service life. Therefore, seismic assessment of existing RC building is a major issue in structural engineering and construction management, and the related seismic analyses should take into account the effect of material ageing and degradation. This paper proposes a practice-oriented procedure for quantifying seismic reliability, taking into account the main effects of carbonation-induced degradation phenomena. It summarizes the main aspects of the most up-to-date models for the seismic degradation of concrete and RC members and shows how nonlinear static (pushover) analyses can be utilized (in lieu of the most time-consuming non-linear time history analyses) in quantifying seismic reliability with respect to the performance levels of relevance in seismic engineering. A relevant case study is finally considered with the aim to showing how some parameters, such as exposure class and cover thickness, affect the resulting seismic reliability of existing RC buildings.
Published: 11 October 2021
by MDPI
Applied Mechanics, Volume 2, pp 797-819; https://doi.org/10.3390/applmech2040046

Abstract:
Due to growing demands on newly developed products concerning their weight, sound emission, etc., advanced materials are introduced in the product designs. The modeling of these materials is an important task, and a very promising approach to capture the viscoelastic behavior of a broad class of materials are fractional time derivative operators, since only a small number of parameters is required to fit measurement data. The fractional differential operator in the constitutive equations introduces additional challenges in the solution process of structural models, e.g., beams or plates. Therefore, a highly efficient computational method called Numerical Assembly Technique is proposed in this paper to tackle general beam vibration problems governed by the Timoshenko beam theory and the fractional Zener material model. A general framework is presented, which allows for the modeling of multi-span beams with general linear supports, rigid attachments, and arbitrarily distributed force and moment loading. The efficiency and accuracy of the method is shown in comparison to the Finite Element Method. Additionally, a validation with experimental results for beam systems made of steel and polyvinyl chloride is presented, to illustrate the advantages of the proposed method and the material model.
Published: 7 October 2021
by MDPI
Applied Mechanics, Volume 2, pp 781-796; https://doi.org/10.3390/applmech2040045

Abstract:
In many applications constant or piecewise constant refractive index profiles are used to study the scattering of plane electromagnetic waves by a spherical object. When the structured media has variable refractive indices, this is more of a challenge. In this paper, we investigate the morphology dependent resonances for the scattering of electromagnetic waves from two concentric spheres when the outer shell has a variable refractive index. The resonance analysis is applied to the general solutions of the radial Debye potential for both transverse magnetic and transverse electric modes. Finally, the analytic conditions to determine the resonance locations for this system are derived in the closed form of both modes. Our numerical results are provided with discussion.
Published: 2 October 2021
by MDPI
Applied Mechanics, Volume 2, pp 766-780; https://doi.org/10.3390/applmech2040044

Abstract:
Published: 1 October 2021
by MDPI
Applied Mechanics, Volume 2, pp 739-765; https://doi.org/10.3390/applmech2040043

Abstract:
Polymer electrolyte coated carbon fibres embedded in polymeric matrix materials represent a multifunctional material with several application scenarios. Structural batteries, thermal management materials as well as stiffness adaptive composites, made from this material, are exposed to significant joule heat, when electrical energy is transferred via the carbon fibres. This leads to a temperature increase of up to 100 K. The thermal behaviour of this composite material is characterized in this numerical study based on a RVE representation for the first time. Compared to classical fibre reinforced plastics, this material comprises a third material phase, the polymer electrolyte coating, covering each individual fibre. This material has not been evaluated for effective thermal conductivity, specific heat and thermal behaviour on the microscale before. Therefore, boundary conditions, motivated from applications, are applied and joule heating by the carbon fibres is included as heat source by an electro-thermal coupling. The resulting temperature field is discussed towards its effect on the mechanical behaviour of the material. Especially the temperature gradient is pronounced in thickness direction, leading to a temperature drop of $1\phantom{\rule{3.33333pt}{0ex}}\frac{{}^{\circ }\mathrm{C}}{\mathrm{mm}}$, which needs to be included in thermal stress analysis in future thermo-mechanically coupled models. Another important emphasis is the identification of suitable homogenization and model reduction strategies in order to reduce the numerical effort spent on the thermal problem. Therefore, traditional analytical homogenization methods as well as a newly proposed “Two-Level Lewis-Nielsen” approach are discussed in comparison to virtually measured effective quantities. This extensive comparison of analytical and numerical methods is original compared to earlier works dealing with PeCCF composites. In addition, the accuracy of the new Two-Level Lewis-Nielsen method is found to fit best compared to classical methods. Finally, a first efficient and accurate 2D representation of the thermal behaviour of the PeCCF composite is shown, which reduces computational cost by up to 97%. This benefit comes with a different Temperature drop prediction in thickness direction of $1.5\phantom{\rule{3.33333pt}{0ex}}\frac{{}^{\circ }\mathrm{C}}{\mathrm{mm}}$. In the context of future modelling of multifunctional PeCCF composite materials with multiphysical couplings, this deviation is acceptable with respect to the huge benefit for computational cost.
Published: 30 September 2021
by MDPI
Applied Mechanics, Volume 2, pp 728-738; https://doi.org/10.3390/applmech2040042

Abstract:
A series of experiments were carried out for developing a paint coating removal method for high-strength bolted joints in steel bridges. The paint-coated bolted joint specimens were heated to the target temperature of 200 °C by using a sheet-type ceramic heater. The maximum temperature of specimens could be controlled within 10% of the target value. The paint coating was easily removed by using general tools after heating. The behaviour of bolts with thermal expansion and shrinkage was monitored by strain gauges attached to the bolts during heating. It was estimated that the axial forces of the bolts were reduced by 2.6% of the initially installed axial forces, on average.
Published: 29 September 2021
by MDPI
Applied Mechanics, Volume 2, pp 694-713; https://doi.org/10.3390/applmech2040040

Abstract:
In this study, an innovative composite was fabricated in which the matrix is partially derived from natural sources and the filler from undervalued eggshell waste material. The effect of coating eggshells and mineral limestone with 2 wt.% stearic acid on the mechanical properties of a bio-epoxy matrix was investigated. Eggshells and limestone (untreated and stearic acid-treated) fillers were added to the bio-epoxy matrix in quantities of 5, 10, and 20 wt.% loadings using a solution mixing technique. The CaCO3 content in eggshells was confirmed to be 88 wt.%, and the crystalline phase was found to be calcite. The stearic acid coating did not show any decrease in crystallinity of the fillers. Scanning electron microscopy (SEM) displayed changes in the fractured surfaces, which infers the fillers altered the bio-epoxy polymer. The mechanical property results showed enhancements in the composite tensile modulus and flexural modulus compared to the pure bio-epoxy, as expected. In contrast, despite the improvement in the tensile and flexural strengths of the stearic acid-treated fillers, the composite strength values were not higher than those of the unfilled bio-epoxy matrix. The energy absorbed by all composites in Charpy impact tests fell below that of the pure bio-epoxy and decreased with an increase in filler content for both untreated and stearic acid-treated fillers tested at 23 and −40 °C. Statistical analysis of the results was conducted using Statistical Analysis Software (SAS) with ranking based on Tukey’s method. The study identified that the addition of 5, 10, and 20 wt.% in a bio-epoxy matrix may be acceptable provided the end product requires lower tensile and flexural load requirements than those of the pure bio-epoxy. However, filler loadings below 5 wt.% would be a better choice.
Published: 29 September 2021
by MDPI
Applied Mechanics, Volume 2, pp 714-727; https://doi.org/10.3390/applmech2040041

Abstract:
A heat treatment is effective for reducing the residual stress of the welded structures. A post-weld heat treatment (PWHT) requires a large heating apparatus (furnace). It requires a high energy, a long time, and a high cost. For examining the possibility of cost and energy saving in PWHT work, an economical and mechanical investigation of the local PWHT to stiffened plate members in steel bridges was conducted. The expense of apparatus for the furnace PWHT was 1.5 times higher than that of local PWHT by sheet-type ceramic heaters. When the number of heater units was reduced and were repeatedly used, the expense for the apparatus became lower. However, it took longer to complete the heat treatment than with the furnace PWHT or the local PWHT with full heater units. The thermal elastic-plastic finite element (FE) analysis examined the effect of local PWHT. The tendency of the stress distribution after the local PWHT differed from the welding residual stress or the stress after the furnace PWHT because of the temperature difference between the heated and the non-heated parts of the local PWHT. However, the effect of residual stress relief by the local PWHT could be almost the same as that of the furnace PWHT.
Published: 28 September 2021
by MDPI
Applied Mechanics, Volume 2, pp 681-693; https://doi.org/10.3390/applmech2040039

Abstract:
This paper deals with the modal analysis of optimized trapezoidal stiffened plates with simple supported conditions on the four edges of the base plate. The main objective of the finite element analysis is to investigate the natural frequencies and mode shapes of some stiffened structures subjected to lateral pressure and uniaxial compression in order to identify any potentially dangerous frequencies and eliminate the failure possibilities. The natural frequencies and mode shapes are important parameters in the design of stiffened plates for dynamic loading conditions. In this study, the numerical analysis is performed for such a design of this kind of welded plates which have already been optimized for lateral pressure and uniaxial compression. The objective function of the optimization to be minimized performed with the Excel Solver program is the cost function which contains material and fabrication costs for Gas Metal Arc Welding (GMAW) welding technology. In this study, the eigenvalue extraction used to calculate the natural frequencies and mode shapes is based on the Lanczos iteration methods using the Abaqus software. The structure is made of two grades of steel, which are described with different yield stress while all other material properties of the steels in the isotropic elastic model remain the same. Drawing the conclusion from finite element analysis, this circumstance greatly affects the result.