Mechanics Based Design of Structures and Machines

Article	Citations
Static, buckling, and free vibration characteristics of porous skew partially functionally graded magneto-electro-elastic plate	79
Analysis of steady-state dynamics and stability of particle dampers considering the friction effect	47
Statement of Retraction: Nonlinear dynamics simulation of the composite reinforced annular system using harmonic differential quadrature framework	37
Static and free vibration response of FGM plates using higher order shear deformation theory and strain-based finite element formulation	35
The influence of various methods of reinforcing circular perforations on the deformability of a welded plate girder with a corrugated web	33
Distribution of the residual tolerable imbalance between correction plans	32
Fatigue life analysis of the radial cylindrical roller bearings: roller end-flange construction effect	31
Retraction	28
Energy loss comparison between kinematically equivalent mechanisms: Slider-crank and eccentric cam	28
An investigation into the effects of profile shifts on helical gear mesh stiffness	24
Dynamic analysis for mechanical system with clearance joint considering dependent interval parameters	24
A parameterized level set method for structural topology optimization using the approximate re-initialization scheme	24
Identification of excitation frequencies of a vibrating beam using Dynamic Mode Decomposition	24
Design and kinematic analysis of cable-driven underactuated manipulator on spacecraft	23
Modeling of counter-bore and counter-sink screw lap joints	22
Comparative study of different porosity models for the nonlinear free vibration analysis of the functionally graded cylindrical panels	22
A 2D problem of thermoviscoelastic half-space subjected to harmonically varying heating using state-space formulation	21
Effect of material distribution on bending and buckling response of a bidirectional FG beam exposed to a combined transverses and variable axially loads	21
Studies on a statically determinate leveling control strategy for a statically indeterminate four-leg support vehicle-borne platform	21
Effect of asymmetric proof mass and size-dependency in flexoelectric nanoharvester subjected to base and restraint forces	20
Coupled and partial impacts of the inclination angle of the discharge boom and the mass of conveyed material on the dynamic behavior of the stacker superstructure	20
Influence of circular cutouts and elastic foundation on vibration characteristics of porous sandwich FGM plates under hygro-thermal environments	20
Topology optimization design for thermal buckling criterion with the size effect	20
Influence of self-weight on buckling and post-buckling behavior of AFGM spring-hinged cantilever column under tip load	19
Logarithmic and trigonometric porosity distributions in rotating functionally graded viscoelastic tapered disk	19

Application of nonlinear energy sink for vibration suppression of mine boring machines	19
A study on static bending behavior of partially elastically supported functionally graded plate with porous voids and prediction of deformation through deep learning	18
Complibot: A compliant external pipe climbing robot	18
Vibration of five-layered sandwich beam with foam/GOAM cores and fiber-reinforced polymer composite face sheet/intermediate layers	18
An analytical study of thermal environment’s effect on the free vibration of FGM double curved FG shells	17
Large deflection response of functionally graded porous structures considering geometrical nonlinearity using an improved FSDT	17
Post buckling responses of carbon nanotubes’ fiber reinforced and nanoclay modified polymer matrix hybrid composite plate under in-plane buckling load using the higher order shear deformation theory	17
Modeling and dynamic analysis of a robotic arm with pneumatic artificial muscle by transfer matrix method	17
Quasi-3D nonlinear flexural response of isogeometric functionally graded CNT-reinforced plates with various shapes with variable thicknesses	17
Buckling analysis of graphene nanoplatelets/polymer composite sandwich cylindrical shells with auxetic honeycomb core under external pressure	16
Application of multi-optimizer neural network in predicting the time-variant response of the dynamic systems	16
Continuous dependence and convergence for a Moore-Gibson-Thompson thermoelastic problem	16
Temperature and porosity-driven nonlinear frequency shifts in functionally graded nanobeams: A comparative analytical study	16
Nonlinear vibrations of a cantilevered conical beam with axially functionally graded material carrying a longitudinally loaded mass	16
Energy efficiency enhancement of SCORBOT ER-4U manipulator using topology optimization method	16
A unified synthesis method for timing-path generation of planar four-bar linkages	16
Nonlinear behaviour of epoxy and epoxy-based nanocomposites: an integrated experimental and computational analysis	15
Studies on multi-frequency synchronization of two pairs of counter-rotating exciters in a split drive double-body vibrating system	15
Investigation on free vibration behavior of laminated angle ply shell with numerical validation	15
Optimization of cutout characteristics in AISI 1045 steel plates for high-cycle fatigue life extension	15
Experimental and finite element analysis of utilizing rectangular and trapezoidal piezoelectric energy harvester with arrays of auxetic cells	14
Non-linear vibration and parametric optimization of sandwich composite curved shell panels with graphene reinforced skins and auxetic honeycomb core	14
Practical solutions for global buckling analysis in tall buildings: classic sandwich continuous model	14
Free vibration of spinning stepped functionally graded circular cylindrical shells in a thermal environment	14
Optimizing seismic fragility assessments for high-speed railway track bridges: a novel multi-parameter methodology and intensity measure selection	14
A percussion-type piezoelectric vibration energy harvester	13
Mesh antenna cable net form finding optimization by an improved NSGA-II	13
Damage identification in functionally graded material beam structures based on frequency analysis and AOA-ANN	13
Accurate free and forced vibration behavior prediction of functionally graded sandwich beams with variable cross-section: A finite element assessment	13
Operational deflection of a three-dimensional shaft with dual stiffness	13
Sustainable design of train seats using finite element analysis and multiobjective optimization	13
Improving moment-capacity of strengthened mono-symmetric and doubly symmetric steel beams using carbon-fiber-reinforced plastic composite plates	13
Uplift derailment for near-fault high speed train-track-hybrid control cable-stayed bridge system	12
The study on the overloading effect on fatigue crack growth considering residual stress relaxation in Al 5456-H38	12
Nonlinear postbuckling analysis of functionally graded graphene origami-enabled auxetic metamaterial plates with bi-directionally stepped thickness	12
The analysis of pressurized FGM cylinders with arbitrarily varying material properties using strain based approach	12
Finite element framework for static analysis of temperature dependent IHSDT based functionally graded CNT reinforced plates	12
Effects of rear seat design on occupant injury risk during frontal crashes: A parametric study using finite element analysis	12
Statement of Retraction: Static analysis of the FG with spatial coordinates cylindricalnanoshells in thermal environment	12
Nonlocal strain gradient-based dynamic stability of functionally graded piezoelectric nanoshells considering thermo-electro-mechanical coupling effects	12
Periodic cavity configurations for effective vibration isolation on base frame: Numerical and experimental analysis	12
Static and dynamic response analysis of corrugated core sandwich plates under patch loading	11
Modeling the through-thickness shear effect in fracture prediction for the SPIF process	11
Wind-induced structural behavior and optical performance of a lightweight composite-based paraboloidal solar dish	11
Effects of modification on the strength–weight ratio of standard bevel gears	11
Thermoelastic creep evolution in a variable thickness functionally graded piezoelectric rotating annular plate considering convection and radiation heat transfer	11
Risk assessment of initial crack propagation in bearing steel based on finite element analysis and machine learning	11
Energy absorption improvement of a cylindrical sandwich structure with auxetic core	11
Meshless method and experimental analysis of hyperelastic plates using Mooney-Rivlin strain energy function subjected to concentrated loading	11
Stress wave propagation analysis of 2D-FGM axisymmetric finite hollow thick cylinder	11

Numerical analysis of lattice core sandwich plates by two-step finite element method	11
Analytical solutions for strain-driven Timoshenko nanobeam bending using generalized functions	11
The dynamic contact of a viscoelastic coated half-plane under a rigid flat punch	10
Anti-loosening mechanism of pitch difference bolt nut connections based on Junker loosening test	10
On exploiting the architecture of annual ring growth for developing a new class of bio-inspired composites	10
Thermal deformations analysis of large-scale vertical Lathe	10
Structural topology optimization for plastic-limit behavior of I-beams, considering various beam-column connections	10
On the mechanics of shear deformable micro beams under thermo-mechanical loads using finite element analysis and deep learning neural network	10
Dynamic analysis of prismatic auxetic trigonometric rotating blades integrated by GNPs-reinforced layers	10
Elastokinematic design and optimization of the multi-link torsion axle – a novel rear axle concept for BEVs	10
Parametric vibration analysis of sector plates using perturbation technique	10
Statement of Retraction: A comprehensive parametric study for hygro-thermal-vibration characteristics of the rotary composite microdisk system	10
Nonlinear vibrations of a linkage mechanism: theory and experiment	10
Exploring wave propagation and attenuation in a metamaterial bar using dual-action vibration absorber with multifrequency resonators	10
Topology and material optimization of an underactuated robot for gait rehabilitation	10
Convex optimization framework with drift control strategies for simulating joints with clearance and friction	10
Dynamic and quasi-static behavior of laminated FG-CNTRC viscoelastic double-curved shells	10
Dynamic analysis of spatial parallel mechanism with spherical pair lubrication clearance under fuzzy parameters	9
Map construction method for granary inspection robots	9
Large-amplitude vibration analysis of FG rectangular plates under rapid cooling	9
Nonlinear vibration analysis of functionally graded porous circular plates under hygro-thermal loading	9
Comments on: “Dynamic response of functionally graded plates resting on two-parameter-based elastic foundation model using a quasi-3D theory” [Mechanics Based Design of Structures and Machines	9
Stability analysis of imperfect functionally graded CNTs reinforced curved beams	9
Numerical analysis of bio-inspired foam-filled multi-cell tapered tubes for energy absorption	9
A comprehensive analysis of in-plane functionally graded plates using improved first-order mixed finite element model	9
Definition of the shear strains in the analysis of soft materials and robots	9
Flexibility analysis of typical roof diaphragms in steel structures using the equivalent connectors method	9
Effects of base material and magnetic field on the dynamic response of MR-laminated composite structures	9
Assessment of porosity influence on thermo-mechanical stability characteristics of skew functionally graded plates using higher order shear deformation theory	9
Nonlinear vibration of fractional piezoelectric layered plates rested on viscoelastic support using DQM	8
Propagation and scattering of Rayleigh wave from an interfacial crack in a viscoelastic waveguide layer bonded to a piezoelectric substrate	8
Nonlocal buckling analysis of double-walled carbon nanotubes using initial value method and matricant approach	8
Deterministic and stochastic flexural behaviors of laminated composite thin-walled I-beams using a sinusoidal higher-order shear deformation theory	8
Transient analysis of bio-inspired shear and normal deformable laminated composite plates using a higher-order finite element model	8
Effects of design parameters on the static responses of two-way beam string structure	8
Numerical simulation of fatigue crack growth in an engine heat shield	8
Friction behavior of 3D printed flexible cavity structure at low-speed condition	8
A Semi-Analytical numerical non-stationary creep analysis of a rotating disk made of Polyamid66 under mechanical and thermal loads	8
Design and performance analysis of an inertial multi-steady state energy sink for torsional vibration mitigation in shaft systems	8
Exploring the vibration and energy absorption characteristic of auxetic tubular structure: an experimental analysis	8
A nonlinear optimal control approach for multi-DOF redundant robotic manipulators	8
Post-buckling analysis of CNT-reinforced hybrid FG plates using MTSDT	8
Analysis and matching of key aerodynamic parameters of the aerodynamic plate braking coach car	8
Three-dimensional analysis of FG-CNTRC shell subjected to internal pressure utilizing Carrera Unified Formulation	8
On linear and nonlinear bending of functionally graded graphene nanoplatelet reinforced composite beams using Gram-Schmidt-Ritz method	8
Synchronous control of lifting and lowering of tunneling machine based on the high-speed digital proportional valve	8
Development and research of diaphragm hydrolic diode for positive displacement pumps	8
A variable nonlocal strain gradient theory for wave propagation analysis of infinite FGP nanosheet with surface effects in hygro-thermal environment	8
Dynamic Stability Analysis of Periodic Loaded Rotating Conical Shells using Floquet Exponent Method	8
A solution for vibration analysis of truck cabin	8
Parameter and sensitivity reliability analysis of curved composite box beam	8
Theoretical modeling and vibration prediction of a spinning graphene nanoplatelet reinforced cylindrical shell internal attached with a beam	8
Refined quasi-3D shear deformation theory for buckling analysis of functionally graded curved nanobeam rested on Winkler/Pasternak/Kerr foundation	8
Machine learning assisted buckling analysis of cantilever bio-inspired helicoidal laminated composite cylindrical shells with cutouts	7
Large amplitude vibration of sandwich beams with GPLRC face sheets and porous core under moving load	7
Crushing analysis and crashworthiness characteristics of auxetic metamaterials: design space exploration with multi-objective optimization	7
Numerical study of snow accumulation on bogies for long marshalling high-speed trains	7
Assessment of contact forces and stresses, torque ripple and efficiency of a cycloidal gear drive and its involute kinematical equivalent	7
Stability analysis of a spinning soft-core sandwich beam with CNTs reinforced metal matrix nanocomposite skins subjected to residual stress	7
A planar bisection strategy for multipoint path synthesis of four-bar linkages	7
Investigation of the effect of structural damping on wind turbine wind-induced fatigue loads	7
Architected tunable twist-compression coupling metastructures based on a generative parametric design for energy absorption and effective mechanical properties	7
Exact solution for free vibration analysis of non-uniform thickness functionally graded porous nanosheet with surface effect based on variable nonlocal and length-scale parameters	7
Analytical investigation of the combined influence of magnetostriction and bandwidth on parametric noise-induced chaos in shape memory alloy micro-electromechanical cantilevers	7
Sandwich composite material analysis for its application in electric rickshaw leaf spring	7
Moment method-based reliability analysis of random vibration in rolling bearings under insufficient probability information	7
Nonlinear vibration and resonance analysis of a rectangular hyperelastic membrane surrounded by nonlinear elastic foundation	7
Analytical solution on magneto-electro-elasto-hygrothermal coupling in rotating functionally graded piezoelectric/piezomagnetic cylinders on Winkler elastic foundation	7
Analytical solution of the electro-magneto-elasto-hydrothermal coupling problem of rotating functionally graded piezoelectric/piezomagnetic hollow spheres under a hydrothermal environment	7
Thermo-electro-mechanical investigation of the rectangular composite plate with nano-silver coating subjected to the external voltage	7
Nonlinear vibration analysis of geometrically imperfect FGM Timoshenko beams with porosity and elastically restrained ends in thermal environments	7
Effects of perforated creases on the mechanical behavior and fatigue life of thick origami structures	7
An experimental study on the bending fatigue behavior of concrete beams by a proposed machine	7
Nonlinear thermal vibration and postbuckling of shear deformable porous FGM circular plates with geometric imperfection and elastic edge restraint	7
Development of exhaust gas insulation system for quarry diesel locomotives	7
Thermomechanical behavior of lattice structures: An analytical, numerical, and experimental study	7
Strain gradient vibration analysis of piezoelectric composite microplate reinforced with FG-GPLs based on sinusoidal shear deformation theory	7
A comparative analysis of various mechanical properties of nano-graphene reinforced polymer composite: As an orthopedic implant substitute of femur bone	7
Thermo-mechanical vibration response of biocompatible sandwich nanoplates with a metamaterial hexachiral auxetic structure	7
Enhancing the prediction accuracy of real-world seismic data using various Decision tree-based models	6

Thermo-elasticity displacement formulation for constrained articulated mechanical systems	6
Vibration and stability analysis of drivelines with self-excitation of non-constant velocity couplings	6
Aero-Hygro-Thermoelastic size-dependent analysis of NCMF-reinforced GNPs sector microplates located between piezoelectric patches in supersonic flow considering surface stress effects	6
Adjustable Wave-like Robot (AWR): design, analysis, and experiment	6
Analyzing of continuous and discontinuous contact problems of a functionally graded layer: theory of elasticity and finite element method	6
Energy absorption and crushing behavior of protective bionic sandwich tubes under axial compression	6
A closed-form solution for dynamic analysis of auxetic sandwich cylindrical structures with FG face sheets under moving pressure	6
Optimization of brake disk wear loss due to brake pad structure	6
Tree-type hybrid mechanism configuration synthesis based on modular decomposition and power-concentrated joint closed-loop design	6
A new probabilistic long-period critical excitation procedure for isolated building structures	6
Optimum synthesis of mechanisms with uncertainties quantification throughout the maximum likelihood estimators and bootstrap confidence intervals	6
A packing problem approach to grasping with a two-finger gripper with application in forest harvesting	6
Precise modeling and stress response analysis of the aero-engine clamp: A simulation and experimental study	6
Reliability assessment of the mining monorail crane drive system under heavy load and steep slope conditions	6
The effects of coolant on the cutting temperature, surface roughness and tool wear in turning operations of Ti6Al4V alloy	6
Research on influence mechanism of prefabricated hole on life extension of compressor impeller	6
Transversely isotropic effects on vibrational behavior of annular sectorial porous plate under in-plane loading	6
The method of task-driven structural synthesis for the creative design of the planar manipulator	6
Statement of Retraction: Application of particle swarm optimization, and genetic algorithm methods for maximizing the phase velocity in the multi-layer nanoscale system	6
Nonlinear vibration analysis of a pyramid lattice sandwich plate in subsonic airflow	6
Numerical assessment of bending and buckling analysis of sigmoid functionally graded (S-FGM) porous plates in framework of secant hyperbolic shear deformation theory: A finite element study	6
Natural characteristic analysis of cracked blade and its application in crack localization	6
Nonlocal thermoelasticity: Transient heat conduction effects on the linear and nonlinear vibration of single-walled carbon nanotubes	6
Approximate modeling of cross-beam multi-axis force/moment sensor through Gaussian process and partial dependence plots for design optimization including stress topology	6
Closed form linear membrane solution for metal-FRP toroidal pressure vessels	6
A novel isogeometric model for free vibration, buckling, and transient response of double-layer BFGP curved beams with elastic boundary condition using modified first-order shear theory	6
Thermo-mechanical interactions in a functionally graded orthotropic thermoelastic medium with rotation and gravity	6
Stochastic FEM-based thermal buckling of SMA fiber-reinforced composite laminated plate using polynomial chaos	6
An active trailer steering design for long combination vehicles	6
Prediction of bridge structure deformation and strain based on dynamic testing and intelligent algorithms	6
Consideration of surface roughness during the design of internal structures for fluid transport produced by additive manufacturing of PEEK	6
Nonlinear vibration suppression of S-S and C-C laminated composite cylindrical shells with magnetostrictive strips	6
Torsional buckling response of FG porous thick truncated conical shell panels reinforced by GPLs supporting on Winkler elastic foundation	6
Nonlinear bending of FG metal/graphene sandwich microplates with metal foam core resting on nonlinear elastic foundations via a new plate theory	6
Nonlocal quasi-3d vibration/ analysis of three-layer nanoplate surrounded by Orthotropic Visco-Pasternak foundation by considering surface effects and neutral surface concept	6
Identification of damping as the main dynamic property of a heavy machine tool body	6
Incorporating bearing flexibility into a digital twin for supervised machine learning-based ball bearing diagnostics	6
Higher-order assumed strain finite element model for the analysis of three-layer FG sandwich plates	6
Free vibration and supersonic flutter analyses of a sandwich cylindrical shell with CNT-reinforced honeycomb core integrated with piezoelectric layers	6
Experimental biomechanical investigation of surrogate headforms equipped with Patka helmet against high-velocity ballistic impact	6
Design, rapid manufacturing and modeling of a reduced-scale forwarder crane with closed kinematic chain	6
On the free vibration characteristics of multiscale hybrid conical panels utilizing Chebyshev–Ritz route	6
Non-linear primary resonance analysis of stiffened FGM conical panels resting on viscoelastic foundation	6
Cutout effects on the dynamic analysis of laminated composite plates resting on two-parameter elastic foundation	5
Enhanced design parameters of a cylindrical helical compression spring using an optimization algorithm and a non-linear behavior model	5
Repair of damaged composite materials after patching experimental investigation of influencing factors	5
Static and thermal instability analysis of embedded functionally graded carbon nanotube-reinforced composite plates based on HSDT via GDQM and validated modeling by neural network	5
A method to develop a high-fidelity gearbox thermal model based on limited temperature measurements	5
Numerical modeling and experimental investigation on the effect of rotation speed on microstructural evaluation and mechanical properties of copper during friction stir processing	5
Conjoined twins 3RPRS: a novel parallel spatial robot	5
Statistical investigation on the coupling mode characteristics of a blade-disk-shaft unit	5
Non-linear assessment of tunable vibrating ring micro-gyroscopes design	5
Poroelastic size dependent dynamics of viscoelastic microbeams connected via a viscoelastic layer	5
Mesh stiffness modeling and dynamic simulation of spur gears with body crack under speed fluctuation condition	5
Fracture analysis of edge-cracked FGM plate with thermo-mechanical loadings using XFEM	5
Free vibration and nonlinear transient analysis of functionally graded graphene origami-enabled auxetic metamaterial cylindrical shells: Analytical and artificial neural network approaches	5
Numerical and experimental analysis of free vibrations and static bending of a sandwich beam with a hyperelastic core	5
Effects of tooth root cracks on vibration and dynamic transmission error responses of asymmetric gears: A comparative study	5
Dynamic response analysis of a shaft-disk-drum rotor system with interval uncertainties	5
Analytical study of electro-mechanical parameters on Love wave in an imperfectly bonded VPCM layered structure	5
Performance analysis of composite laminates wing skin with the aid of fluid structure interaction of aerodynamic loading-structural analysis	5
Free vibration behavior in functionally graded material plates with dual efficient quadrilateral finite elements	5
Vibration damping by enhancing of magneto-rheological damper performance using novel smart fluid	5
Modification of wavelet-based downsampling method to reduce computational error in nonlinear dynamic analysis	5
Wave propagation analysis of cylindrical sandwich shell with auxetic core utilizing first-order shear deformable theory (FSDT)	5
Dexterity distribution design for attitude adjustment of multi-joint robotics based on singularity-free workspace decomposition	5
Finite element and artificial neural network-based dynamic analysis of viscoelastic sandwich beams on elastic foundation	5
Design of compliant flexural beam negative Poisson’s ratio structures based on spatial hexahedron feature points method	5
Static and dynamic buckling analysis of two-layer shells include auxetic honeycomb core combined with laminated three-phase polymer/GNP/fiber surface resting on Kerr elastic medium in hygro-thermal en	5
A new method of micro-slip contact normal pressure modeling and its application in the dynamic analysis of the dovetail–tenon–mortise jointed blades	5
Bending and free vibration analysis of FG circular plates using a five unknown high order shear deformation theory	5
A novel analytical-based viewpoint for MEMS mass spring system: systematic design guideline for dimensional tolerance and footprint reduction powered by dimensionless analysis	5
A smooth-guiding method for aerodynamic drag reduction on key regions of a high-speed train	5
Crashworthiness analysis of hierarchically reinforced double-square tubes under axial impact	5
Chaotic dynamics of supersonic fluttering porous FG-plate on a nonlinear pasternak foundations under sub-harmonic resonance	5
A semi-analytical methodology for predicting the vibroacoustic response of functionally graded nanoplates under thermal loads	5
Reliability-based simultaneous optimization of quantities, positions, and parameters of inerter-based vibration absorbers to minimize the probability of building failure during earthquakes via the CIO	5
Influence of local stiffeners and non-uniform edge loads on the stability characteristics of composite laminates with a circular opening	5
Influence law of subgrade differential settlement on longitudinal ballastless track irregularity considering interlayer contact stiffness randomness	5
Active prediction compensation strategy: A new positioning compensation technique for improving the accuracy of the dual ball screw feed mechanism under load	5
Computer-aided digitization method for structural synthesis of planar non-fractioned kinematic chains with pure revolute joints	5
Dynamic analysis and performance assessment of a vibratory feeder for different motor positions on trough	5
Dynamic optimization of anchor points positions in a cable driven exosuit: a computer simulation approach	5
Nonlinear postbuckling and snap-through instability of movable simply supported BDFG porous plates rested on elastic foundations	5
Integrated design algorithm for branching structures	5
Influence of cracks on the nonlinear dynamic behaviors of pipes conveying fluid	5
Power generation performance of a bistable speed bump vibration energy harvester	5
An innovative application of double slider-crank mechanism in efficient of the scanning acoustic microscopy system	5
Free and forced thermomechanical vibration and buckling responses of functionally graded magneto-electro-elastic porous nanoplates	5
Dynamic characteristics of laminated composite CNT reinforced MRE cylindrical sandwich shells using HSDT	5
Optimizing plastic shredder rotor design through structural finite element analysis: A comprehensive approach using experimental design and response surface methodology	5
Stress and frequency optimization of prismatic sandwich beams with structural joints: Improvements through accelerated topology optimization	5
Design analysis and development of a gantry robot for multi-layer 3-D concrete printing with simulation and experimental validation	5
Dynamic modeling of closed-chain robotic manipulators in the presence of frictional dynamic forces: A planar case	4
Retracted Article: Bending performance of a multi-phase initially stressed plate considering interaction force	4