The consideration of compliance of structural joints in calculation of large panel buildings

The article presents and analyzes the design solutions of horizontal and vertical joints, as well as methods for determining the coefficient of compliance joints. It also presents the numerical determination of the coefficients of compliance of the horizontal mortar joint in accordance with the standards for the design of large-panel buildings. It is shown that the compliance of the joint on the embedded parts consists of the compliance of the connecting element, embedded parts of the wall panels, namely the metal plate and reinforcing bars of the anchors, as well as the compliance of the welds. In this case, the joint operates in a complex stress-strain state. It is noted that the most difficult is to determine the compliance of embedded parts. Three calculation methods have been developed for the numerical determination of the compliance coefficients of anchor bars under the action of tension (compression), bending moment and shear forces on the embedded part. The deformation of the welds was defined in MGSU in the framework of the experimental research of the work of the vertical seam with embedded parts. The article presents a graph of the deformation in the weld on the applied vertical load on the test piece.

Simulation of slitting method for calculation of compliance functions of laminated composites

In this research, the process of slitting with an assumed residual stress distribution is simulated to calculate compliance functions of laminated composites. The primary aim of this article is to investigate different parameters influencing the calculation of compliance coefficients for laminated composites using a finite element model. First, using two- and three-dimensional finite element models, the process of slitting in isotropic materials for calculating the compliance coefficients is simulated. The results show a complete agreement between the two models. Also, the results of simulation show that in the modeling of slitting method for laminated composites, real slit width must be considered. That is because composite laminates are generally thin and slitting in these materials results in large slit width to thickness ratio. Finally, the developed simulation method is applied to calculate compliance coefficients for two carbon/epoxy- and glass/epoxy-laminated composites with quasi-isotropic and cross-ply lay-ups using a three-dimensional finite element modeling. For a better precision, a full three-dimensional model without symmetry assumption is considered. The presented method is capable of simulating slitting method in parts and specimens with complicated geometry as well as in orthotropic materials with any degree of orthotropy.

The Influence of Multiple Piezoelectric Effects on Elastic Coefficient of Piezoelectric Ceramics

The development of new materials and the performance improvement of existing materials become an important subject from different aspects. In this paper, based on the theoretical research results of multiple piezoelectric effects, the influence of multiple piezoelectric effects on elastic coefficient of piezoelectric ceramics is studied. Theoretical analysis indicates that it is multiple piezoelectric effects that make piezoelectrics have two kinds of elastic and they result in the decrease of elastic compliance coefficients. Experimental validation is performed through PZT-5. Experimental results show that elastic compliance coefficient grows decreased by 0.912 times.

Elasticity

All solids change shape under mechanical force. Under small stresses, the strain x is related to stress X by Hooke’s Law (x) = (s)(X), or the converse relationship (X) = (c)(x). The elastic compliance coefficients (s) are generally reported in units of m2/N, and the stiffness coefficients (c) in N/m2. For a fairly stiff material like a metal or a ceramic, c is about 1011 N/m2 = 1012 dynes/cm2 = 100 GPa = 0.145 × 108 PSI. Hooke’s Law is a linear relation between stress and strain, and does not describe the elastic behavior at high stress levels that requires higher order elastic constants (Chapter 14). Irreversible phenomena such as plasticity and fracture occur at still higher stress levels. Two directions are needed to specify stress (the direction of the force and the normal to the face on which the force acts), and two directions are needed to specify strain (the direction of the displacement and the orientation of the measurement axis). Thus there are four directions involved in measuring elastic stiffness, which is therefore a fourth rank tensor: . . . Xij = cijklxkl . . . .

Thermodynamic relationships

In the next few chapters we shall discuss tensors of rank zero to four which relate the intensive variables in the outer triangle of the Heckmann Diagram to the extensive variables in the inner triangle. Effects such as pyroelectricity, permittivity, pyroelectricity, and elasticity are the standard topics in crystal physics that allow us to discuss tensors of rank one through four. First, however, it is useful to introduce the thermodynamic relationships between physical properties and consider the importance of measurement conditions. Before discussing all the cross-coupled relationships, we first define the coupling within the three individual systems. In a thermal system, the basic relationship is between change in entropy δS [J/m3] and change in temperature δT [K]: . . . δS = CδT, . . . where C is the specific heat per unit volume [J/m3 K] and T is the absolute temperature. S, T, and C are all scalar quantities. In a dielectric system the electric displacement Di [C/m2] changes under the influence of the electric field Ei [V/m]. Both are vectors and therefore the electric permittivity, εij , requires two-directional subscripts. Occasionally the dielectric stiffness, βij , is required as well. . . . Di = εijEj Ei = βijDj. . . . Some authors use polarization P rather than electric displacement D. The three variables are interrelated through the constitutive relation . . . Di = Pi + ε0Ei = εijEj. . . . The third linear system in the Heckmann Diagram is mechanical, relating strain xij to stress Xkl [N/m2] through the fourth rank elastic compliance coefficients sijkl [m2/N]. . . . xij = sijklXkl. . . . Alternatively, Hooke’s Law can be expressed in terms of the elastic stiffness coefficients cijkl [N/m2]. . . Xij = cijklxkl. . . . When cross coupling occurs between thermal, electrical, and mechanical variables, the Gibbs free energy G(T, X, E) is used to derive relationships between the property coefficients. Temperature T, stress X, and electric field E are the independent variables in most experiments.

A Variational Approach for Modeling Flexibility Effects in Manipulator Arms

SUMMARYThis paper presents a general technique to model flexible components (mainly links and joints flexibilities are considered) of manipulator arms based on Castigliano's theorem of least work. The robotic arms flexibility properties are derived and represented by the matrix of compliance coefficients. Such expressions can be used to determine the errors due to the robotic tip deformations under the application of a set of applied loads at the tip in a Cartesian space. Once these deformations are computed, they may be used to correct for the positional errors arisen from the robotic structural deformations in the motion control algorithms.

A Variational Approach for Modeling Flexibility Effects in Manipulator Arms

This paper presents a general technique to model flexible components (mainly links and joints flexibilities are considered) of manipulator arms based on the Castigliano’s theorem of least work. The robotic arms flexibility properties are derived and represented by the matrix of compliance coefficients. Such expressions can be used to determine the errors due to the robotic tip deformations under the application of a set of applied loads at the tip in Cartesian space. Once these deformations are computed, they may be used to correct for the positional errors arisen from the robotic structural deformations in the motion control algorithms.