Strain State Research Articles

Numerical Analysis of Soil Deformation in Earth Dams Using a Stiffness Variation Technique

Small earth dams have been used since ancient times and are often the main source of water in semi-arid regions. In this particular type of engineering work, soils saturated by water present changes in their mechanical properties (especially in the first filling), which usually cause a simultaneous loss of stiffness and shear strength. In this context, the software UNSTRUCT presents itself as a very useful tool, as it allows calculating the final state of stress x strain for a plane strain state, using the Finite Element Method, both for saturated and unsaturated embankments, considering an elastic model and the effect of suction (and its variation), through a stiffness variation technique. The present research used UNSTRUCT to assess the behavior of the embankment of a hypothetical earth dam, varying the features of its typical cross-section: homogeneity; internal drainage structures; geometry along a longitudinal profile; and the influence of the compaction level. The results showed that the soil responded better to strains for the scenario of better compaction along the dry branch of the compaction curve, as well as with the use of a vertical drainage element. It was also observed that the strains were higher when greater sections considered, which, in a real situation, would cause distortions along the longitudinal profile of the dam. The software UNSTRUCT proved to be efficient in obtaining and visualizing the modeling results, also making it possible to analyze the development of failure over time after the dam was filled. With UNSTRUCT, a more realistic analysis of the behavior of the hypothetical dam – considering factors that are specific to unsaturated soils – was possible. Worth mentioning also that the software allowed the appraisal of multiple changes in the dam’s geometry and parameters.

Effects of short-term aging on the mechanical and structural performance of hot mix asphalt mixtures: a case study complemented by statistical analysis

This study aimed to assess the effects of short-term aging on the mechanical behaviour of asphalt layers of flexible pavement structures. The effects of aging on their mechanical performance have not yet been detailed, in terms of structural analyses. Therefore, pavement structures with distinct types of asphalt layers (non-aged and aged) were evaluated. Stability, tensile strength, resilient modulus, fatigue behaviour and permanent deformation or static creep were determined. The mePADS software was used to carry out structural analyses of the pavements, based on variations in the bound layers’ mechanical properties, loading level and tire inflation pressure. Horizontal stresses and strains were determined at the bottom of the binder course. Fatigue lives were predicted and discussed based on statistical analyses. The short-term aging enhanced the mechanical parameters, but adversely affected the fatigue life for the examined strain states, which reinforces the importance of carrying out the structural analyses.

A comprehensive methodology to estimate the fatigue life of S-shaped integral squeeze film damper

The Integral Squeeze Film Damper (ISFD) finds widespread application in various rotating machinery, such as gas turbines, turbochargers, and high-speed rotors, to dampen vibrations and improve operational stability. This study presents a comprehensive methodology to predict the fatigue life of an Integral Squeeze Film Damper (ISFD) by combining Low Cycle Fatigue (LCF), High Cycle Fatigue (HCF) test, and Finite Element (FE) simulations. An S-shaped spring specimen is designed and tested under high-cycle fatigue loading to develop the stress amplitude versus the number of the cycles curve. LCF tests are performed to obtain fatigue parameters, and a Chaboche kinematic hardening model is employed for cyclic plasticity FE simulations. FE analysis of the ISFD is conducted to establish its dynamic characteristics, aiding in identifying critical locations based on maximum von Mises stress. The integration of local stress–strain states from FE simulations with experimental fatigue parameters is carried out to predict fatigue life of ISFD. The validity of the methodology is confirmed through experimental and stress analyses, providing valuable insights for optimizing the fatigue performance of ISFD components.

Radon Emanation and Dynamic Processes in Highly Dispersive Media

The paper considers a dispersive geological medium (seismically turbid medium, as defined by A.V. Nikolaev), which is in a stress–strain state. Results of studies on the joint monitoring of seismic effects and radon emanation in various geological environments are presented. It is concluded that the turbidity of the medium, as a statistical characteristic, can be generalized in terms of other media parameters, such as permeability. A stable connection between radon emanation and dynamic processes occurring in a geological environment and caused by external influences has been established. The concentration of radon can also reflect the degree of enrichment of the environment by underground fractures. Consequently, saturation of the environment with radon provides information about the presence of disturbances in a geological environment in the form of cracks and a stress–strain state of the medium before and after seismic loadings. Radon observations make it possible to assess a continuity of the environment and the possibility of leaching in natural conditions. Therefore, it could be efficiently used for underground leaching efficiency assessment.

Experimental and theoretical study on high-temperature creep of VT6 titanium alloy under multi-axial loading conditions

In the framework of damage mechanics, we discuss a new mathematical model that describes the kinetics of the stress–strain state and damage accumulation during material degradation by the mechanism of long-term strength under complex multiaxial stress state. An experimental and theoretical technique is proposed for determination of material parameters and scalar constitutive functions for damaged media based on specially set experiments on laboratory specimens. The results of experimental studies and numerical simulations of short-term high-temperature creep of VT6 titanium alloy under uniaxial and multiaxial loading are presented. Numerical results are compared with the data obtained through experiments. Particular attention is paid to simulating the process of unsteady creep for complex deformation modes, accompanied by rotation of main areas of stress, strain and creep strain tensors. It is shown that the developed version of the constitutive relations of the damaged media enables us to describe the processes of unsteady creep and long-term strength of structural alloys under multiaxial stress with the accuracy sufficient for engineering calculations.

Prosthetic framework improvement using lattice structure: A comparative finite element study of a mandibular implant-supported prosthesis

Objectives:An alternative option was proposed regarding the prosthetic rehabilitation of a fully edentulous mandible using only four implants. The aim was to reduce the stiffness of the prosthetic framework. To that end, the alternative option consists of a prosthetic framework optimized with a porous structure. Mechanical differences were analyzed between non-prosthetic mandible and restored mandible either with a conventional bulk titanium framework or with this alternative option. The non-prosthetic mandible corresponds to the mandible in its natural state, without prosthesis. This will be considered as the reference for comparison with restored models (mandible with prosthesis). Methods:Three models are used: the first one is the non-prosthetic mandible, the second one is the restored mandible with conventional bulk titanium prosthetic framework, and the third one is the alternative option. Prosthetic framework was optimized with the use of a lattice structure. A numerical analysis was performed (with Abaqus Standard software®) to obtain the effective parameters corresponding to equivalent homogeneous behavior. In the 3 models, physiological boundary conditions were used, considering the activity of several muscles of the masticatory system during three main tasks of mastication (incisive clenching, maximum intercuspation and unilateral molar clenching). Results:Numerical simulations allowed to obtain mandibular global kinematics, local displacement at the bone–implant interface and the state of strain at the bone–implant interface, for each masticatory tasks. For this comparative study, the non-prosthetic mandible model was used as a reference to observe the benefits of using a lattice prosthetic framework compared to a conventional bulk titanium framework. Conclusion:Compared to conventional titanium framework, the lattice prosthetic one appeared to be more respectful of the natural mandible kinematics, given by the reference model. It also resulted in strain values within the physiological loading range.

The digital twin use for modeling the multi‐storey building response to seismic impacts

AbstractThis work is dedicated to theoretical and experimental research on constructing a digital twin for a 24‐story building located in a seismic zone with the possibility of seismic vibrations of up to eight on the Richter scale. A digital model of the building was developed considering the changes in its geometry (damage or absence of structural elements). This requires detailed field inspections of partially constructed buildings and consideration of the inspection results when constructing a digital model. The boundary conditions, in addition to the geometric characteristics of the building, include the physical and mechanical characteristics of all its structural elements obtained through nondestructive testing methods. Discrepancies between the structural elements' design and actual concrete classes were identified. The initial conditions included real accelerograms at the location of the building, which served as input data for the direct dynamic analysis. Thus, there is a need to develop a hybrid system for modeling the stress–strain state of a 24‐story building that uses information technologies (Internet of Things) with sensors during research. Such an IoT system, combined with one information network using cloud technologies, allows us to obtain the necessary information in real‐time, highlighting the features of the building (the second stage of constructing the digital twin). The bar and spatial models of buildings with distributed parameters of structural stiffness at bending and shear and the mass and mass moment of inertia were considered. The results of numerical studies of the first form of natural vibrations for the building rod (according to the expressions obtained by the authors) and spatial models (performed using the LIRA‐CAD software package developed in Ukraine based on the finite element method) are presented. A comparison with the first experimental form of natural vibrations confirmed that considering the moment of inertia of the building mass makes it possible to determine the ordinates of the self‐form of vibrations and seismic horizontal loads more accurately. The experimental first frequency and form of natural vibrations of a 24‐story residential building in Odesa were obtained from the results of vibration monitoring at the construction stage (16 floors were erected) and after all 24‐floor erection. The direct dynamic method of building calculations for seismic effects specified by earthquake accelerograms was used along with the method proposed by the authors to consider damping during forced building vibration calculations and the actual physical and mechanical characteristics of concrete and reinforcement obtained by non‐destructive testing methods. The calculated vibration amplitudes at the top of the building cantilever model were compared with the damping parameters obtained using the Voicht model and the authors' method under the influence of an accelerogram recorded during the powerful 1977 Bucharest earthquake with an epicenter in the Vrancea area (Romanian Carpathians).

410 Improving Patient Outcomes through Design of Biodegradable Implants for Long Bone Fractures

OBJECTIVES/GOALS: Current long bone fracture standard of care uses inert metal intramedullary nails (IMN), 10x stiffer than femur cortex. Consequent “stress-shielding” bone loss sees >5% of patients needing revision surgery. To improve nonunion healing, we develop automated design optimization methods for biodegradable Mg alloy IMNs to control local reloading. METHODS/STUDY POPULATION: Finite element analysis (FEA) is performed on 3D bone-IMN representations to establish this study’s baseline strain states for existing inert IMN geometries within QCT-informed femoral models under simulated biomechanical loading. FEA with Mg alloy properties for same IMN designs simulate transient IMN material loss through discrete time-step models with experimental in vivo Mg corrosion rates and strain-based bone density evolution using remodeling algorithms from literature. Transient stability and strength metrics, fracture zone stress profiles under gradual reloading and manufacturing constraints are formulated through gradient-based sensitivity analysis into a topology optimization framework (TOF) incorporating a reaction-diffusion degradation model to generate IMN topologies. RESULTS/ANTICIPATED RESULTS: TOF designs for Mg alloy IMNs with transient allowable strength constraints, using safety factors to prevent IMN failure, demonstrate higher compliance than standard inert IMNs with mechanical properties closer to native cortical bone. The biodegradation model within the TOF, informed by corrosion behavior from bone-IMN FEA study, predicts how potential design evolutions affect transient strain states of the system. Thus, local fracture region stress states are controlled by the algorithm optimizing for desirable transient stiffness profiles based on a minimum variance objective of fracture zone stress compared to a target bone stress profile. Optimized IMNs with porous, high surface area features achieve 50% decrease in IMN stiffness over 6 months recovery time and complete in vivo degradation in 24 months. DISCUSSION/SIGNIFICANCE: Our TOF reduces “stress-shielding” effects via design for controlled IMN biodegradation to gradually increase fracture zone loading, stimulating remodeling and reducing current risk of post-operative fracture and surgical removal in ~15k cases/yr. in the U.S. In vitro mechanical and in vivo clinical testing is required to validate design results.

Interpretable structure-property correlation in X-ray diffraction patterns of HfZrO thin films via machine learning

The X-ray diffraction (XRD) patterns of materials contain important and rich information in terms of structure, strain state, grain size, etc. The XRD can become a powerful fingerprint for material characterizations when it is combined with machine learning techniques. Attempts utilizing machine-learning-based methods mainly focus on phase identification for mixture compounds. Herein, we applied a machine-learning-based method linking XRD patterns of HfZrO thin films directly to their electronic properties in experiments. In accordance with conventional understanding, the machine learning model suggests that non-monoclinic (NM) phases of HfO2 and ZrO2 are among the main contributors to higher relative permittivity and lower leakage current. Furthermore, some minor interfacial phases like TiO x and ZrN x are also proposed to be even more important contributors to our target electronic properties. Our research demonstrates that machine learning has the potential to reveal minor XRD signals from sub-1 nm interfacial layers that have long been considered undetectable and thus ignored by human interpretation.

Application of the Green's function method for static analysis of nonlocal stress-driven and strain gradient elastic nanobeams

This paper focuses on the static analysis of a generally restrained Euler-Bernoulli nanobeam (GRNB), which is subjected to arbitrary distributed or concentrated loads. The small length scale effect is introduced through a strongly nonlocal integral elastic law called the stress-driven nonlocal Euler-Bernoulli beam model, and a weakly nonlocal elastic law called the strain-gradient Euler-Bernoulli beam model. The stress-driven nonlocal theory and the strain gradient elasticity theory are both employed, to formulate the differential equation governing the Euler-Bernoulli nanobeams. Both theories are ruled by a similar 6th order differential equation, with distinct higher-order boundary conditions. The paper demonstrates that the strain gradient theory can be also reformulated as a stress-driven nonlocal theory with unsymmetrical kernel, in contrast to the initial stress-driven nonlocal theory which has symmetrical exponential kernel. Additionally, some theoretical backgrounds about both nonlocal elasticity theorems are provided. Exact solutions for both nanobeam models are presented, using Green's function method. The parameters of the Green's functions are derived for each beam theory, and then utilized to establish the static displacement function of both nanobeam theories. Exact solutions are provided for the bending of both nanobeams with various end boundary conditions, that account for the small length scale effects. The paper also compares the responses of the stress-driven Euler-Bernoulli beam and the strain gradient Euler-Bernoulli beam, showing close deflections and similar effects of increasing the nonlocal parameter on beam stiffness. A major difference highlighted between the two theories is that the strain gradient theory predicts a homogeneous strain state for homogeneous stress state, as opposed to the stress-driven theory.

Graphene as the anti-oxidation protective layer: How good or bad can it be?

This study investigates the conditional anti-oxidation layer of graphene on Cu and its variation of morphology and strain state, demonstrating that the oxidation process could be divided into two stages. The chemical vapor deposition (CVD) growth and a high-humidity environment were exploited to observe the Cu foil oxidizing with the protection layer of graphene. The observation of optical microscopy (OM) and scanning electron microscopy (SEM) reveals the sequence process of the anti-oxidation layer of graphene on the diverse Cu orientations. Except for the wrinkles on graphene and orientations of Cu, the vacancies in the graphene play a crucial role in anti-oxidation. Furthermore, the oxidation of underlying Cu deteriorates the quality of graphene and reduces the strength of interaction at the graphene/Cu interface. The oxidation of graphene-capped Cu is divided into two stages: (i) The attenuated graphene/Cu interaction due to the Cu oxidation beneath, and (ii) the generation and enlargement of CuO particles damage the adjacent graphene, as clearly observed in the OM and SEM images. The time evolution analysis using angular-resolved photoelectron spectroscopy (ARPES) offers robust evidence to support the worse quality of graphene and the decoupling between graphene and Cu foil after the oxidation process. X-ray photoelectron spectroscopy (XPS) and Raman spectroscopy express that the defects are created by the degradation of graphene rather than the generation of external functional groups. Thus, the Cu oxidation simultaneously influences both the substrate (Cu) and the protective layer (graphene), substantially weakening the graphene/Cu interaction.

Experimental study and theoretical analysis on ballast particle crushing based on energy dissipation and release

Existing particle crushing models and crushing criteria relying on the stress–strain state have the limitations of inaccuracy and single crushing behavior. It is well known that energy is the essential factor that drives particle crushing. This paper aims to reveal the crushing process of ballast particles more accurately from the perspective of energy. In this study, a series of single-particle uniaxial compression tests (SPUCT) were conducted using a high-speed camera system. The multi-stage crushing behavior and crushing characteristics of the particles have then been investigated. Energy state during particle crushing was analyzed. Finally, an energy-based multi-stage crushing model and crushing criterion for particles were proposed and validated by performing SPUCT on 10 new particles. The results show that: there is a significant difference between the characteristic stress-characteristic strain states when particles with similar shapes and sizes are crushed, the proposed multi-stage crushing theory accurately explains this complex crushing behavior; The evolution of the input energy, strain energy, and dissipation energy of the particles is consistent with the crushing characteristics; The energy-based multi-stage crushing model can avoid the limitation of using the characteristic stress-characteristic strain states, and the energy-based multi-stage crushing criterion can effectively capture the crushing behavior of particles. This study is very helpful in elucidating the mechanism of particle crushing from the perspective of energy evolution.

Investigation on low hydrostatic stress extrusion technology for forming of large thin-walled components with high ribs

An increase in hydrostatic stress improves the plasticity of metallic materials. However, for some special components, such as large thin-walled components with high ribs, excessive hydrostatic stress can cause several problems that make it impossible to prepare such components using plastic forming methods. In this study, the effect of hydrostatic stress on the deformation behavior of large thin-walled components with high ribs was investigated using a combination of numerical simulations and theoretical derivations. The results indicated that excessive hydrostatic stress leads to die failure, causing metal flow difficulties, uneven deformation, inconsistent mechanical properties, and reduced forming accuracy. Therefore, a low-hydrostatic-stress extrusion method was proposed by adjusting the contact friction, metal flow direction and displacement, and force boundary conditions to reduce the hydrostatic compressive stress. These principles are mainly reflected in the following three aspects: First, the size of the difficult deformation zone was reduced by changing the friction conditions from dry friction to fluid friction or boundary friction to reduce the frictional resistance. Second, the high-stress zone was eliminated by changing the metal flow direction, adjusting the strain state from unidirectional to multi-directional flow, shortening the metal flow path, and reducing the metal flow resistance. Third, the strong compressive stress state in the three directions was weakened by regulating the force boundary conditions and changing the loading method from one-way extrusion to multi-directional loading. Based on these principles, a series of new forming technologies have been developed, such as actively counteracting frictional resistance, slotting, and ditching on dies for long-lasting lubrication, multi-directional short-range metal flow, drawing-assisted extrusion, and multi-directional active loading. The adoption of these technologies realizes the labor-efficient formation of large thin-walled components with high ribs and provides the formed members with high precision and uniform mechanical properties.

Large Polarization Near 50 μC/cm2 in a Single Unit Cell Layer SrTiO3.

The generally nonpolar SrTiO3 has attracted more attention recently because of its possibly induced novel polar states and related paraelectric-ferroelectric phase transitions. By using controlled pulsed laser deposition, high-quality, ultrathin, and strained SrTiO3 layers were obtained. Here, transmission electron microscopy and theoretical simulations have unveiled highly polar states in SrTiO3 films even down to one unit cell at room temperature, which were stabilized in the PbTiO3/SrTiO3/PbTiO3 sandwich structures by in-plane tensile strain and interfacial coupling, as evidenced by large tetragonality (∼1.05), notable polar ion displacement (0.019 nm), and thus ultrahigh spontaneous polarization (up to ∼50 μC/cm2). These values are nearly comparable to those of the strong ferroelectrics as the PbZrxTi1-xO3 family. Our findings provide an effective and practical approach for integrating large strain states into oxide films and inducing polarization in nonpolar materials, which may broaden the functionality of nonpolar oxides and pave the way for the discovery of new electronic materials.

Feasibility Study of Experimental Protocol for the Time-Dependent Mechanical Response of Synthetic Tibia.

In this research, an experimental biomechanics construct was developed to reveal the mechanics of distal tibial fracture by submitting synthetic tibiae to cyclic loading, resulting in a combined stress state due to axial compression and bending loads. The synthetic tibia was fixed at the knee but allowed to rotate in the coronal and sagittal planes at the ankle. The first three loading regimes lasted for 4000 cycles/each, and the final until ultimate failure. After 12k±80 cycles, the observed failure patterns closely resembled distal tibial fractures. The collected data during cyclic loading were fitted into a phenomenological model to deduce the time-dependent response of the synthetic tibiae. Images were also collected and analyzed using digital image correlation to deduce the full-field state of strain. The latter revealed that longitudinal strain contours extended in the proximal-distal direction. The transverse strain contours exemplified a medial-to-lateral distribution, attributed to the combined contributions of the Poisson's effect and the flexural deformation from axial and bending components of the applied load, respectively. The experimental construct, full-field characterization, and data analysis approaches can be extended to elucidate the effect of different fixation devices on the overall mechanical behavior of the bone and validate computational models in future research.

Non-equilibrium nature of fracture determines the crack paths

Local kinetic processes during crack growth are non-equilibrium and discrete and thus cannot be resolved in the framework of continuum thermodynamics. Atomistic modeling using existing empirical or machine-learning force fields also fails to offer satisfactory solutions for the lack of sufficient accuracy in predicting the energetics of strong lattice distortion and edge cleavage during fracture. The problem is addressed here by using a high-fidelity neural network-based force field for fracture (NN-F3) that covers the space of strain states up to material failure and the non-equilibrium, intermediate states at the crack tip. Atomistic simulations using NN-F3 reveal spatial complexities from lattice-scale kinks to sample-scale crack patterns in 2D crystals such as graphene, which evolve along the process of crack growth. The non-uniform lattice distortion and undercoordination of cleaved edges at the crack front play critical roles in the fracture process. The fracture toughness by cleaving specific edges thus cannot be quantified by their energy densities with relaxed atomic-level structures, which, however, have been widely used in the literature. Instead, the fracture patterns, the critical stress intensity factors corresponding to the kinking events, and the energy densities of edges in the intermediate, unrelaxed states offer reasonable measures for the fracture resistance and its anisotropy, which can be determined from experimental or simulation data with the atomic-level resolution. The findings conform well with recent experimental observations.

Strain Solitons in an Epitaxially Strained van der Waals-like Material.

Strain solitons are quasi-dislocations that form in van der Waals materials to relieve the energy associated with lattice or rotational mismatch. Novel electronic properties of strain solitons were predicted and observed. To date, strain solitons have been observed only in exfoliated crystals or mechanically strained crystals. The lack of a scalable approach toward the generation of strain solitons poses a significant challenge in the study of and use of their properties. Here, we report the formation of strain solitons with epitaxial growth of bismuth on InSb(111)B by molecular beam epitaxy. The morphology of the strain solitons for films of varying thickness is characterized with scanning tunneling microscopy, and the local strain state is determined from atomic resolution images. Bending in the solitons is attributed to interactions with the interface, and large angle bending is associated with edge dislocations. Our results enable the scalable generation of strain solitons.

Enhancement of Perpendicular Magnetic Anisotropy in Tm3Fe5O12(111) Epitaxial Films via Synergistic Stoichiometry and Strain Engineering

AbstractEstablishing a reliable control of perpendicular magnetic anisotropy (PMA) is challenging but essential for the full utilization of rare‐earth iron garnets in spintronic devices. In this study, a feasible approach to enhance the PMA of ferrimagnetic thulium iron garnet (TmIG) films is presented. This approach involves precise adjustments in cation stoichiometry and epitaxial strain state. By fine‐tuning the pre‐ablation process and oxygen partial pressure during pulsed laser deposition, a series of high‐quality TmIG films can grow with variable cation stoichiometry, i.e., the Tm/Fe molar ratio. The finding reveals that cation stoichiometry plays a crucial role in determining the magnetic properties of the TmIG films. Particularly, the stoichiometric TmIG film has the strongest PMA due to the maximized magnetostriction coefficient. Combining this stoichiometry optimization and strain engineering, an unprecedented PMA strength of ≈30 kJ m−3 for TmIG is achieved. This achievement demonstrates a simple and effective method for harnessing the magnetic properties of rare‐earth iron garnet films, paving the way for their advanced applications in next‐generation spintronic devices.

Probabilistic notch fatigue assessment under size effect using micromechanics-based critical distance theory

Geometrical discontinuities are inevitable in engineering structures due to various functional requirements, which often yield complex stress–strain state and thereby significantly impact their fatigue performances. In this study, crystal plasticity theory is coupled with traditional critical distance theory for notch effect modelling considering microstructural heterogeneity. Specifically, microstructural and geometrical size effects on critical distance and fatigue performance are studied based on Sub-modelling approach. In addition, critical distance theory is coupled with Weibull distribution for probabilistic fatigue life evaluation of notched components. The developed method is verified and compared by using experimental data of GH4169 alloy. The findings demonstrate that the evaluated P-S-N curves exhibit strong agreement with tested data and geometrical size effect poses larger influence than the grain size effect on critical distance and fatigue life.

Nonlinear deformations of size-dependent porous functionally graded plates in a temperature field

In this paper, the Variational Iteration Method (VIM) or Extended Kantorovich Method (EKM) is formulated for the first time for flexible porous functionally graded (PFGM) plates with different boundary conditions and geometric nonlinearity according to the theory of Theodore von Karman. Its accuracy and efficiency are demonstrated. The plate is subjected to a uniform transversal load and temperature field. The displacement field of the plate is approximated based on the classical plate theory (CTP) or Kirchhoff's plate theory. The governing equations are derived using Hamilton's principle. Modified Coupled Stress Theory (MCST) is used to account for size-dependent effects. The material properties vary with thickness and are temperature dependent. Four porosity distribution patterns are considered in this study. Several examples are solved to demonstrate the proposed algorithm. The results obtained are compared with solutions obtained by the Bubnov-Galerkin Method (BGM) in higher approximations, the Finite Difference Method (FDM) of second order accuracy, as well as with results obtained by the Finite Element Method (FEM) of other authors. The results include an analysis of the effect of size dependent parameters, porosity type pattern, porosity index, functionally graded index, temperature field and different types of boundary conditions on the stress–strain state and bending deflection of plates.