Based on the dynamical equation, the constitutive relation and the strain-displacement relation, the vibration equation of small deflection beams was derived.

Element-free Galerkin Method for the analysis of 2D geometrical nonlinearities is presented by means of geometrically nonlinear strain-displacement relation under small strain assumption.

The relative displacement is obtained by subtracting the convecting displacement from the displacement, which makes it possible to adopt linear strain-displacement relationship in element local coordinate.

In this paper, the aeroelastic model of composite panel with thermal effects is established using von Karman large deformation strain-displacement relationship, piston theory of aerodynamics and quasi-steady theory of thermal stress.

Based on the shell theory and the first order shear deformation theory, an accurate strain-displacement relationship of the helicoidal structure modeled is derived. An energy equilibrium equation of free vibration is introduced by the principle of virtual work. Applying the Rayleigh-Ritz method an analytical eigenvalue equation is formulated and solved the vibration characteristics of the helicoidal structure are obtained by an efficient computational approach.

On the foundation of nonlinear displacement field, the FEM discrete method is applied, and the Kane's method is utilized in deriving the equations of motion.

Based on the relationship,strain-displacement and constitution law,of elastic stress-strain,along with motion balance equation,the transport equations in 2-D and 3-D transversely isotropio medut ore derived using coordinate transformation and SVD (Singular Value Decomposition) technique .

From the strain-displacement relations in the three-dimensional nonlinear elasticity theory, the displacements are expressed by the trigonometric series representation through the thickness of the plate.

A 21-DOF beam finite element,including transverse shear DOF and warping DOF,is developed for analysis. The governing differential equations of motion for a hingeless rotor are derived using the Hamilton's principle.

On the basis of exact strain-displacement relation, equations of motion for flexible multibody system are derived by using virtual work principle.

The strain-displacement relation of the von Karman's large deflection theory is employed to describe the geometric non-linearity and the aerodynamic piston theory is employed to account for the effects of the aerodynamic force.

Based on precise strain-displacement relation, the geometric stiffening effect is taken into account, and the rigid-flexible coupling dynamic equations are derived using velocity variational principle.

In this paper, the Lagrangian description was used as a strain-displacement relation.

The mathematical description of the wave propagation includes a parabolic strain-displacement relation which enables the methodology to consider non-linear material responses where the strain is less than about 30%.

An accurate strain-displacement relationship based on the thin-shell theory combined with the finite element method using triangular plate elements with three nodes and nine degrees of freedom for each node is utilized.

The axial displacements of an initially crooked, simply supported column, subjected to an axial compressive force at its end, are determined by using several variants of the axial strain-displacement relationship.

Geometric nonlinearity is accounted for as deformations and deformation rates are evaluated by using the Green-Lagrange strain-displacement relationship.

Using the exact finite strain-displacement relationship, the Eulerian strains ?xE, ?yE and γxyE were computed.

The specimen design is sufficiently simple that a closed-form expression for the strain-displacement relationship has been successfully developed.

In this paper, variational principles in elasticity are classified according to the differences in the constraints used in these principles. It is shown in a previous paper[4] that the stress-strain relations are the constraint conditions in all these variational principles, and can not be removed by the method of linear Lagrange multiplier. The other possible constrants are four of them: ( 1 ) equations of equilibrium, ( 2 ) Strain-displacement relations, ( 3 ) boundary conditions of given external forces and...

In this paper, variational principles in elasticity are classified according to the differences in the constraints used in these principles. It is shown in a previous paper[4] that the stress-strain relations are the constraint conditions in all these variational principles, and can not be removed by the method of linear Lagrange multiplier. The other possible constrants are four of them: ( 1 ) equations of equilibrium, ( 2 ) Strain-displacement relations, ( 3 ) boundary conditions of given external forces and boundary conditions of given boundary displacements. In variational principles of elasticity, some of them have only one kind of such constraints, some have two kinds or three kinds of constraints and at the most four kinds of constraints. Thus, we have altogether 15 kinds of possible variationai principles. However, for every possible variational principle, either the strain energy density or the complementary energy density may be used. Hence, there are altogether 30 classes of functionals of variational principles in elasticity. In this paper, all these functionals are tabulated in detail.

Finite strain components of circular plate are derived in the present paper using method of co-moving coordinate system of Chien and Chen[4]. The equations governing large deflection of variable thickness circular plate is then established by variational principle. Instead of dynamic relaxation method by Turvey [1978], infinite power series is used in solving the problem with an aid of a power series[1] is used in solving the problem with the aid of computer. The results show good agreement with Turvey. For...

Finite strain components of circular plate are derived in the present paper using method of co-moving coordinate system of Chien and Chen[4]. The equations governing large deflection of variable thickness circular plate is then established by variational principle. Instead of dynamic relaxation method by Turvey [1978], infinite power series is used in solving the problem with an aid of a power series[1] is used in solving the problem with the aid of computer. The results show good agreement with Turvey. For the convenience of engineering reference, necessary curves are also provided in this paper.

This paper studies large deflection problem of beams and plates by the finite element method. The elongation of the middle surface caused by its rotation is considered in strain-displacenmet relations. The higher order terms will be reserved when strain energy is calculated. The elastic stiffness matrix, linear and nonlinear initial stress stiffness matrices are derived by the principle of minimum potential energy. Examples show that precision will be properly raised although the total storage amount and calculating...

This paper studies large deflection problem of beams and plates by the finite element method. The elongation of the middle surface caused by its rotation is considered in strain-displacenmet relations. The higher order terms will be reserved when strain energy is calculated. The elastic stiffness matrix, linear and nonlinear initial stress stiffness matrices are derived by the principle of minimum potential energy. Examples show that precision will be properly raised although the total storage amount and calculating time are