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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1977

Biaxial load effects on the crack border elastic strain energy and strain energy rate

The validity of the singular solution (first term of a series representation) is investigated for the crack tip stress and displacement field in an infinite sheet with a flat line crack with biaxial loads applied to the outer boundaries. It is shown that if one retains the second contribution to the series approximations for stress and displacement in the calculation of the local elastic strain energy density and elastic strain energy rate in the crack border region, both these quantities have significant biaxial load dependency. The value of the J-integral does not depend on the presence of the second term of the series expansion for stress and displacement. Thus J(I) is insensitive to the presence of loads applied parallel to the plane of the crack.

Eftis, J.↗
DOE OSTI2022

Seismic strain energy partitioning: estimating the strain energy of seismic body waves.

This report details a method to estimate the energy content of various types of seismic body waves. The method is based on the strain energy of an elastic wavefield and Hooke’s Law. We present a detailed derivation of a set of equations that explicitly partition the seismic strain energy into two parts: one for compressional (P) waves and one for shear (S) waves. We posit that the ratio of these two quantities can be used to determine the relative contribution of seismic P and S waves, possibly as a method to discriminate between earthquakes and buried explosions. We demonstrate the efficacy of our method by using it to compute the strain energy of synthetic seismograms with differing source characteristics. Specifically, we find that explosion-generated seismograms contain a preponderance of P wave strain energy when compared to earthquake-generated synthetic seismograms. Conversely, earthquake-generated synthetic seismograms contain a much greater degree of S wave strain energy when compared to explosion-generated seismograms.

58 GEOSCIENCES↗
NASA NTRS1985

Residual thermal and moisture influences on the strain energy release rate analysis of edge delamination

A laminated plate theory analysis is developed to calculate the strain energy release rate associated with edge delamination growth in a composite laminate. The analysis includes the contribution of residual thermal and moisture stresses to the strain energy released. The strain energy release rate, G, increased when residual thermal effects were combined with applied mechanical strains, but then decreased when increasing moisture content was included. A quasi-three-dimensional finite element analysis indicated identical trends and demonstrated these same trends for the individual strain energy release rate components, G sub I and G sub II, associated with interlaminar tension and shear. An experimental study indicated that for T300/5208 graphite-epoxy composites, the inclusion of residual thermal and moisture stresses did not significantly alter the calculation of interlaminar fracture toughness from strain energy release rate analysis of edge delamination data taken at room temperature, ambient conditions.

Obrien, T. K.↗
NASA NTRS1986

Residual thermal and moisture influences on the strain energy release rate analysis of edge delamination

A laminated plate theory analysis is developed to calculate the strain energy release rate associated with edge delamination growth in a composite laminate. The analysis includes the contribution of residual thermal and moisture stresses to the strain energy released. The strain energy release rate, G, increased when residual thermal effects were combined with applied mechanical strains, but then decreased when increasing moisture content was included. A quasi-three-dimensional finite element analysis indicated identical trends and demonstrated these same trends for the individual strain energy release rate components, G sub I and G sub II, associated with interlaminar tension and shear. An experimental study indicated that for T300/5208 graphite-epoxy composites, the inclusion of residual thermal and moisture stresses did not significantly alter the calculation of interlaminar fracture toughness from strain energy release rate analysis of edge delamination data taken at room temperature, ambient conditions.

Obrien, T. K.↗
NASA NTRS1987

Convergence of strain energy release rate components for edge-delaminated composite laminates

Strain energy release rates for edge delaminated composite laminates were obtained using quasi 3 dimensional finite element analysis. The problem of edge delamination at the -35/90 interfaces of an 8-ply composite laminate subjected to uniform axial strain was studied. The individual components of the strain energy release rates did not show convergence as the delamination tip elements were made smaller. In contrast, the total strain energy release rate converged and remained unchanged as the delamination tip elements were made smaller and agreed with that calculated using a classical laminated plate theory. The studies of the near field solutions for a delamination at an interface between two dissimilar isotropic or orthotropic plates showed that the imaginary part of the singularity is the cause of the nonconvergent behavior of the individual components. To evaluate the accuracy of the results, an 8-ply laminate with the delamination modeled in a thin resin layer, that exists between the -35 and 90 plies, was analyzed. Because the delamination exists in a homogeneous isotropic material, the oscillatory component of the singularity vanishes.

Raju, I. S.↗
NASA NTRS1988

Convergence of strain energy release rate components for edge-delaminated composite laminates

Strain energy release rates for edge delaminated composite laminates were obtained using quasi 3 dimensional finite element analysis. The problem of edge delamination at the -35/90 interfaces of an 8-ply composite laminate subjected to uniform axial strain was studied. The individual components of the strain energy release rates did not show convergence as the delamination tip elements were made smaller. In contrast, the total strain energy release rate converged and remained unchanged as the delamination tip elements were made smaller and agreed with that calculated using a classical laminated plate theory. The studies of the near field solutions for a delamination at an interface between two dissimilar isotropic or orthotropic plates showed that the imaginary part of the singularity is the cause of the nonconvergent behavior of the individual components. To evaluate the accuracy of the results, an 8-ply laminate with the delamination modeled in a thin resin layer, that exists between the -35 and 90 plies, was analyzed. Because the delamination exists in a homogeneous isotropic material, the oscillatory component of the singularity vanishes.

Raju, I. S.↗
NASA NTRS1993

Strain energy of thermally stressed multilayer panels and its sensitivity coefficients

A study is made of the effect of lamination and material parameters of thermally stressed multilayer composite panels on the strain energy and its sensitivity coefficients obtained by the three-dimensional thermoelasticity model. The sensitivity coefficients measure the sensitivity of the strain energy to variations in the different lamination and material parameters of the panel. The strain energy and sensitivity coefficients obtained by the three-dimensional model are used as the basis for assessing the accuracy of the corresponding quantities obtained by two-dimensional first-order shear deformation theory. Numerical results are presented for antisymmetrically laminated angle-ply panels subjected to linear temperature variation through the thickness. The numerical results demonstrate the accuracy of the strain energy and its sensitivity coefficients obtained by the first-order shear deformation theory, for the range of parameters considered, and the importance of the particular terms in the strain energy, which vanish for single-layer panels.

Noor, Ahmed K.↗
NASA NTRS1991

Residual thermal and moisture influences on the strain energy release rate analysis of local delaminations from matrix cracks

An analysis utilizing laminated plate theory is developed to calculate the strain energy release rate associated with local delaminations originating at off-axis, single ply, matrix cracks in laminates subjected to uniaxial loads. The analysis includes the contribution of residual thermal and moisture stresses to the strain energy released. Examples are calculated for the strain energy release rate associated with local delaminations originating at 90 degrees and angle-ply (non-90 degrees) matrix ply cracks in glass epoxy and graphite epoxy laminates. The solution developed may be used to assess the relative contribution of mechanical, residual thermal, and moisture stresses on the strain energy release rate for local delamination for a variety of layups and materials.

Obrien, T. K.↗
NASA NTRS1989

A simplified approach to strain energy release rate computations for interlaminar fracture of composites

A simple approach for the strain energy release rate computations based on the finite element method and a singular fitting model is presented. The model uses the stress and displacement distributions at the delamination front. The method is applied to a mixed-mode double cracked-lap-shear composite configuration. The strain energy release rate components predicted by the model are compared with the finite element crack-closure method. The effect of the mesh size on the stress and displacement distribution is isolated. The strain energy release rates predicted by relatively coarse mesh sizes are in good agreement with the finite element crack closure method.

Armanios, Erian A.↗
NASA NTRS1991

On the strain energy of laminated composite plates

The present effort to obtain the asymptotically correct form of the strain energy in inhomogeneous laminated composite plates proceeds from the geometrically nonlinear elastic theory-based three-dimensional strain energy by decomposing the nonlinear three-dimensional problem into a linear, through-the-thickness analysis and a nonlinear, two-dimensional analysis analyzing plate formation. Attention is given to the case in which each lamina exhibits material symmetry about its middle surface, deriving closed-form analytical expressions for the plate elastic constants and the displacement and strain distributions through the plate's thickness. Despite the simplicity of the plate strain energy's form, there are no restrictions on the magnitudes of displacement and rotation measures.

Atilgan, Ali R.↗
NASA NTRS1989

Modal strain energies in COSMIC NASTRAN

A computer program was developed to take a NASTRAN output file from a normal modes analysis and calculate the modal strain energies of selected elements. The FORTRAN program can determine the modal strain energies for CROD, CBAR, CELAS, CTRMEM, CQDMEM2, and CSHEAR elements. Modal strain energies are useful in estimating damping in structures.

Snyder, B. D.↗
NASA NTRS1987

Calculation of strain-energy release rates with higher order and singular finite elements

A general finite element procedure for obtaining strain-energy release rates for crack growth in isotropic materials is presented. The procedure is applicable to two-dimensional finite element analyses and uses the virtual crack-closure method. The procedure was applied to nonsingular 4-noded (linear), 8-noded (parabolic), and 12-noded (cubic) elements and to quarter-point and cubic singularity elements. Simple formulas for strain-energy release rates were obtained with this procedure for both nonsingular and singularity elements. The formulas were evaluated by applying them to two mode I and two mixed mode problems. Comparisons with results from the literature for these problems showed that the formulas give accurate strain-energy release rates.

Raju, I. S.↗
NASA NTRS1986

Simple formulas for strain-energy release rates with higher order and singular finite elements

A general finite element procedure for obtaining strain-energy release rates for crack growth in isotropic materials is presented. The procedure is applicable to two-dimensional finite element analyses and uses the virtual crack-closure method. The procedure was applied to non-singular 4-noded (linear), 8-noded (parabolic), and 12-noded (cubic) elements and to quarter-point and cubic singularity elements. Simple formulas for strain-energy release rates were obtained with this procedure for both non-singular and singularity elements. The formulas were evaluated by applying them to two mode I and two mixed mode problems. Comparisons with results from the literature for these problems showed that the formulas give accurate strain-energy release rates.

Raju, I. S.↗
NASA NTRS1971

On strain energy and constitutive relations for alkali metals.

An expression for the strain energy as a continuous differentiable function of the Green-Cauchy deformation tensor is obtained for the alkali metals at absolute zero temperature. The development is based on well established quantum and classical calculations of the various contributions to the crystal energy. Stress-deformation relations are next obtained. As a check on the accuracy of the strain energy, theoretical calculations of the values of the second-order elastic coefficients are obtained and compared to known experimental data. The predicted values are shown to compare quite well with the experimental values.

Eftis, J.↗
NASA NTRS1993

A method for calculating strain energy release rate based on beam theory

The Timoshenko beam theory was used to model cracked beams and to calculate the total strain energy release rate. The root rotation of the beam segments at the crack tip were estimated based on an approximate 2D elasticity solution. By including the strain energy released due to the root rotations of the beams during crack extension, the strain energy release rate obtained using beam theory agrees very well with the 2D finite element solution. Numerical examples were given for various beam geometries and loading conditions. Comparisons with existing beam models were also given.

Sun, C. T.↗
NASA NTRS1994

Improved method for calculating strain energy release rate based on beam theory

The Timoshenko beam theory was used to model cracked beams and to calculate the total strain-energy release rate. The root rotations of the beam segments at the crack tip were estimated based on an approximate two-dimensional elasticity solution. By including the strain energy released due to the root rotations of the beams during crack extension, the strain-energy release rate obtained using beam theory agrees very well with the two-dimensional finite element solution. Numerical examples were given for various beam geometries and loading conditions. Comparisons with existing beam models were also given.

Sun, C. T.↗
NASA NTRS2008

Optimization of Stability Constrained Geometrically Nonlinear Shallow Trusses Using an Arc Length Sparse Method with a Strain Energy Density Approach

A technique for the optimization of stability constrained geometrically nonlinear shallow trusses with snap through behavior is demonstrated using the arc length method and a strain energy density approach within a discrete finite element formulation. The optimization method uses an iterative scheme that evaluates the design variables' performance and then updates them according to a recursive formula controlled by the arc length method. A minimum weight design is achieved when a uniform nonlinear strain energy density is found in all members. This minimal condition places the design load just below the critical limit load causing snap through of the structure. The optimization scheme is programmed into a nonlinear finite element algorithm to find the large strain energy at critical limit loads. Examples of highly nonlinear trusses found in literature are presented to verify the method.

Hrinda, Glenn A.↗