A solution for 1D non-linear problems for finite elements with full stiffness matrices

Structural analysis of structural parts with stiffness variation can be difficult. The stiffness variation of elements can be modelled by average values of cross-sectional and material parameters and applying the fine FE mesh. For elimination of mentioned disadvantages of classical finite element applications, a two-node nonlinear bar element with the continuous longitudinal variation of stiffness was developed in the first part of the monography. The stiffness matrices of the bar element were derived using full geometric nonlinear nonincremental formulation of equilibrium equations without any linearization. In the second part, the stiffness matrices of geometrically nonlinear beam finite element were derived using full nonlinear nonincremental formulation. The matrices of two-node plane beam element with symmetric cross-section and constant stiffness were formulated. The accuracy of new nonlinear elements were compared and assessed by numerical experiments against ANSYS analyses

Nový prútový konečný prvok pre elektro-tepelné analýzy FGM materiálov

In this contribution, new electro-thermal link finite element for Functionally Graded Materials (FGM) will be presented. Spatial variation of material properties as well as varying convection effect will be considered. FEM equations describing the behaviour of the link element will be based on semi-analytical calculation of ordinary differential equations describing coupled electro-thermal problem.V predkladanom príspevku bude prezentovaný nový elektro-tepelný prútový konečný prvok pre Funkcionálne Gradované Materiály (FGM), pričom bude uvažovaná priestorová premenlivosť materiálových vlastností a pôsobenie premenlivej konvekcie na prút. Budú prezentované nové MKP rovnice opisujúce správanie sa prúta, založené na semi-analytickom výpočte obyčajných diferenciálnych rovníc popisujúcich previazanú elektro-tepelnú úlohu

New coupled thermoelectric link finite element for FGM materials

The paper deals with derivation process of new FEM equations for steady thermoelectric two-way coupled analysis of link conductor made of Functionally Graded Material (FGM). One example of coupled analysis will be introduced to demonstrate accuracy and effectiveness of our new approach in computer modelling of such systems

Ananlysis of actuator made of fgm using new electro-thermo-mechanical finite elements

Actuator is a mechatronic system that transforms one type of energy (e.g. electric energy) into the mechanical displacement and mechanical force (mechanical energy). Nowadays, these actuators can be made of Functionally Graded Materials (FGM) to ensure simple shape of the actuator and to improve its effectiveness, particularly for micro systems. FGM is built as a mixture of two or more constituents which have almost the same geometry and dimensions. The variation of macroscopic material properties can be induced by variation of both the volume fractions and material properties (e.g. by a non-homogeneous temperature field) of the FGM constituents. The paper deals with a new approach in analysing of the systems made of FGM using our new beam finite elements. Multiphysical analysis (weak coupled electro-thermomechanical analysis) and spatial continuous variation of material properties are supported. The analysis of the micro actuator with constant cross section made of FGM is presented in the paper. This simple-shaped actuator is supplied by electric current and the efficiency of the actuator is optimised. The solution results will be compared with those obtained by using solid elements of a FEM commercial program

Piezoelectric finite beam element with FGM core for mechatronic applications

The paper deals with finite beam element with piezoelectric layers and functionally graded material of core. In the paper homogenization of FGM material properties and homogenization of core and piezoelectric layers is presented. In the process of homogenization direct integration method and multilayer method is used. The concept of transfer functions and transfer constants is used for computation of individual submatrices. Functionality of new FGM finite beam with piezoelectric layers is presented by numerical experiments. Static, harmonic and full transient piezoelectric analysis of FGM beams with piezolayers is presented

Modal analysis of the fgm beam-like structures with effect of the thermal axial force

The modal analysis of the FGM beam-like actuator is presented, where effects of the thermal axial force and the shear force are considered. The temperature load is assumed to be lower as the critical buckling temperature. The longitudinal variation of material properties has been assumed which can be caused by the varying constituent’s volume fraction and the temperature dependence of the constituent’s material properties. Our new FGM beam finite element has been used in the proposed analysis. An influence of the material properties variation and the thermal axial forces on the actuator eigenfrequency and eigenform has been studied and discussed

Piezoelektrická analýza saw snímača pomocou metódy konečných prvkov

In this contribution modeling and simulation of surface acoustic waves (SAW) sensor using finite element method will be presented. SAW sensor is made from piezoelectric GaN layer and SiC substrate. Two different analysis types are investigated - modal and transient. Both analyses are only 2D. The goal of modal analysis, is to determine the eigenfrequency of SAW, which is used in following transient analysis. In transient analysis, wave propagation in SAW sensor is investigated. Both analyses were performed using FEM code ANSYS.Príspevok sa zaoberá modelovaním a simuláciou SAW snímača, ktorý využíva šírenie povrchových vĺn, pričom na simulovanie sa využíva metóda konečných prvkov. SAW snímač je zložený z piezoelektrickej GaN vrstvy a z SiC substrátu. Vyšetrované sú dva typy analýz - modálna a prechodová. Cieľom modálnej analýzy je určiť vlastnú frekvenciu SAW snímača, ktorá je následne využitá v prechodovej analýze. V prechodovej analýze sa vyšetruje šírenie sa povrchovej vlny v SAW snímači. Obe analýzy sú realizované v MKP programe ANSYS

A sandwich bar element for geometric nonlinear thermo-elastic analysis

This contribution deals with a two-node straight sandwich composite bar element with constant double symmetric rectangular cross-sectional area. This new bar element (based on the non-linear second-order theory) is intended to perform the non-incremental full geometric non-linear analysis. Stiffness matrix of this composite bar contains transfer constants, which accurately describe polynomial uniaxial variation of the material thermo-physical properties. In the numerical experiments the weak coupled thermo-structural geometric non-linear problem was solved. Obtained results were compared with several analyses made by ANSYS programme. Findings show good accuracy of this new finite element. The results obtained with this element do not depend on the element mesh density

A nonlinear truss finite element with varying stiffness

This contribution deals with a new truss element with varying stiffness intended to geometric and physically nonlinear analysis of composite structures. We present a two-node straight composite truss finite element derived by new nonincremental full geometric nonlinear approach. Stiffness matrix of this composite truss contains transfer constants, which accurately describe the polynomial longitudinal variation of cross-section area and material properties. These variations could be caused by nonhomogenous temperature field or by varying components volume fractions of the composite or/and functionally graded materials (FGM´s). Numerical examples were solved to verify the established relations. The accuracy of the new proposed finite truss element are compared and discused