Stem taper functions for Betula platyphylla in the Daxing’an Mountains,northeast China

Accurate prediction of stem diameter is an important prerequisite of forest management.In this study,an appropriate stem taper function was developed for upper stem diameter estimation of white birch(Betula platyphylla Sukaczev)in ten sub-regions of the Daxing’an Mountains,northeast China.Three commonly used taper functions were assessed using a diameter and height dataset comprising 1344 trees.A first-order continuous-time error structure accounted for the inherent autocorrelation.The segmented model of Max and Burkhart(For Sci 22:283–289,1976.https://doi.org/10.1093/fores tscie nce/22.3.283)and the variable exponent taper function of Kozak(For Chron 80:507–515,2004.https://doi.org/10.5558/tfc80507-4)described the data accurately.Owing to its lower multicollinearity,the Max and Burkhart(1976)model is recommended for diameter estimation at specific heights along the stem for the ten sub-regions.After comparison,the Max and Burkhart(1976)model was refitted using nonlinear mixed-effects techniques.Mixed-effects models would be used only when additional upper stem diameter measurements are available for calibration.Differences in region-specific taper functions were indicated by the method of the non-linear extra sum of squares.Therefore,the particular taper function should be adjusted accordingly for each sub-region in the Daxing’an Mountains.

Large deflection of flexible tapered functionally graded beam

In this paper the semi-analytical analyses of the flexible cantilever tapered functionally graded beam under combined inclined end loading and intermediate loading are studied.In order to derive the fully non-linear equations governing the non-linear deformation,a curvilinear coordinate system is introduced.A general non-linear second order differential equation that governs the shape of a deflected beam is derived based on the geometric nonlinearities,infinitesimal local displacements and local rotation concepts with remarkable physical properties of functionally graded materials.The solutions obtained from semi-analytical methods are numerically compared with the existing elliptic integral solution for the case of a flexible uniform cantilever functionally graded beam.The effects of taper ratio,inclined end load angle and material property gradient on large deflection of the beam are evaluated.The Adomian decomposition method will be useful toward the design of tapered functionally graded compliant mechanisms driven by smart actuators.

Recursive impedance inversion of ground-penetrating radar data in stochastic media

The travel time and amplitude of ground-penetrating radar （GPR） waves are closely related to medium parameters such as water content, porosity, and dielectric permittivity. However, conventional estimation methods, which are mostly based on wave velocity, are not suitable for real complex media because of limited resolution. Impedance inversion uses the reflection coefficient of radar waves to directly calculate GPR impedance and other parameters of subsurface media. We construct a 3D multiscale stochastic medium model and use the mixed Gaussian and exponential autocorrelation function to describe the distribution of parameters in real subsurface media. We introduce an elliptical Gaussian function to describe local random anomalies. The tapering function is also introduced to reduce calculation errors caused by the numerical simulation of discrete grids. We derive the impedance inversion workflow and test the calculation precision in complex media. Finally, we use impedance inversion to process GPR field data in a polluted site in Mongolia. The inversion results were constrained using borehole data and validated by resistivity data.

Development of ecoregion-based merchantable volume systems for Pinus brutia Ten. and Pinus nigra Arnold. in southern Turkey

Estimating individual tree volume is one of the essential building blocks in forest growth and yield models. Ecologically based taper equations provide accurate vol- ume predictions and allow classification by mer- chantable sizes, assisting in sustainable forest management. In the present study, ecoregion-based compatible volume systems for brutian pine and black pine in the three ecoregions of southern Turkey were developed. Several well-known taper functions were evaluated. A second- order continuous-time autoregressive error structure was used to correct the inherent autocorrelation in the hierar- chical data, allowing the model to be applied to irregularly spaced and unbalanced data. The compatible segmented model of Fang et al. （For Sci 46：1-12, 2000） best described the experimental data. It is therefore recommended for estimating diameter at a specific height, height to a specific diameter, merchantable volume, and total volume for the three ecoregions and two species analyzed. The nonlinearextra sum of squares method indicated differences in ecoregion and tree-specific taper functions. A different taper function should therefore be used for each pine spe- cies and ecoregion in southern Turkey. Using ecoregion- specific taper equations allows making more robust esti- mations and, therefore, will enhance the accuracy of diameter at different heights and volume predictions.

A system for calculating the merchantable volume of oak trees in the northwest of the state of Chihuahua, Mexico

The taper functions of Kozak （1988）, Bi （2000） and Fang et al. （2000） were comparatively analyzed in the present paper to develop a system for calculating the merchantable volume of oaks in the northwestern region of the state of Chihuahua （Mexico）. Taper data corresponding to 298 trees were collected in mixed and uneven-aged pine-oak stands located throughout the study area, and covering the cxisting range of ages, stand densities and sites. Results show that the compatible segmented model developed by Fang et al. （2000） best described the experimental data and is therefore recommended for estimating tree diameter at a specific height, height to a specific diameter, merchantable volume, and total volume for oaks. The equation developed in this study is a fundamental tool for use in forest surveys in the study region and is simple enough to ensure its operational implementation. The results of the statistical analysis show that the equation can be recommended for other regions, although some local adaptations may be needed.

Buckling Analysis of Axially Functionally Graded and Non-Uniform Beams Based on Timoshenko Theory

In this paper,the buckling behaviors of axially functionally graded and non-uniform Timoshenko beams were investigated.Based on the auxiliary function and power series,the coupled governing equations were converted into a system of linear algebraic equations.With various end conditions,the characteristic polynomial equations in the buckling loads were obtained for axially inhomogeneous beams.The lower and higher-order eigenvalues were calculated simultaneously from the multi-roots due to the fact that the derived characteristic equation was a polynomial one.The computed results were in good agreement with those analytical and numerical ones in literature.